PoojaMoolya: Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- ||00:01 ||Welcome to this '''tutorial''' on '''Probability and Distributions in GeoGebra'''. |- ||00:08 ||In this '''tutorial''',..."

2020-10-21T07:22:36Z

Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- ||00:01 ||Welcome to this '''tutorial''' on '''Probability and Distributions in GeoGebra'''. |- ||00:08 ||In this '''tutorial''',..."

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{|border=1
||'''Time'''
||'''Narration'''

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||00:01
||Welcome to this '''tutorial''' on '''Probability and Distributions in GeoGebra'''.
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||00:08
||In this '''tutorial''', we will:

Learn how to use '''Probability Calculator''' in '''GeoGebra'''

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||00:16
||Look at different distributions and parameters.
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||00:20
||Here I am using:

'''Ubuntu Linux''' Operating System version 16.04

'''GeoGebra''' 5.0.481.0 hyphen d
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||00:34
||To follow this '''tutorial''', you should be familiar with

'''GeoGebra''' interface, Statistics
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||00:42
||'''Fish Feed'''

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||00:44
||Let us look at an example.

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||00:47
||A fishery is testing four types of feed formulation on its fish: '''A''', '''B''', '''C''' and '''D'''.

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||00:56
||Data to be collected after feeding the fish for 6 months are:

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||01:01
||Length in '''millimeters'''

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||01:04
||Weight in '''pounds'''

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||01:07
||Girth in '''millimeters'''

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||01:10
||Let’s look at some of these data.
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||01:13
||'''Fish Feed Data'''

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||01:15
||We will use these data for our analysis.

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||01:20
||Please download the '''code file''', '''Fishery-data''', provided along with this '''tutorial'''.
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||01:29
||'''Probability'''

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||01:31
||Probability of an event P(A), lies between 0 and 1.

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||01:38
||Statistics are calculated for each sample.

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||01:42
||The probability distribution of these statistics is called a sampling distribution.

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||01:48
||Examples are '''normal''', '''t''' etc.

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||01:53
||Please refer to '''Additional material''' provided along with this tutorial.
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||01:59
||I have opened the '''GeoGebra''' interface.
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||02:03
||Click on '''View''' tool and select '''Spreadsheet'''.
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||02:09
||Click on '''X''' at top right corner of '''Graphics''' and '''Algebra''' views.

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||02:16
||In the '''code file''', use the '''mouse''' to highlight length data in column '''B'''.
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||02:24
||Hold '''Control''' key down and press '''C''' to copy the data.
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||02:30
||Click in the top of the '''Spreadsheet''' in '''GeoGebra'''.
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||02:35
||Hold '''Control''' key down and press '''V'''.
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||02:39
||Drag and adjust the column width.
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||02:42
||As shown earlier in the series, change the name to '''Length milimeter hyphen A'''.

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||02:55
||Adjust the '''column''' width.
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||02:58
||Repeat this with data in '''columns E''', '''H''' and '''K'''.
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|| 03:05
||Select all data in the four '''columns''' by dragging.
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||03:10
||Under the '''menubar''', under '''One Variable Analysis''', click on '''Multiple Variable Analysis'''.
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|| 03:18
||A'''Data Source''' popup window appears.

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||03:22
||Click on '''Analyze''' button.
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||03:25
||A '''Data Analysis''' window appears.
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||03:29
||Drag the boundary to see it properly.
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||03:33
||'''Box plots''' appear for data for all four '''columns'''.
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|| 03:39
||Click anywhere in the '''GeoGebra''' window and then click on '''Show Statistics''' tool.

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||03:48
||'''Statistics''' are displayed below the '''box plots'''.
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||03:53
||Above the statistics, click on '''menu button''' next to the word '''Statistics'''.

Select '''ANOVA'''.
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||04:03
||Drag the boundaries and resize the window to increase size of statistics tables.
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||04:11
||Place the cursor on the boundary below the plots.

And drag to increase the size of the tables.
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|| 04:20
||'''F value''' is the ratio of '''between groups MS''' to '''within groups MS'''.

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||04:28
||Hence, '''F value''' is quite large (36.5892).

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||04:34
||'''P value''' is 0.

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||04:37
||This means it is probably less than 0.001.

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||04:43
||The feed does make a '''statistically significant''' difference to the length of the fish.

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||04:50
||Hence, the '''null hypothesis''' can be rejected in this case.

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||04:56
||The '''null hypothesis''' here is that none of the feeds make any difference to the length of the fish.
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||05:05
||Next to the '''ANOVA display''', click on the '''menu button'''.
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||05:11
||Two options appear for '''T Test''': '''Difference of Means''' and '''Paired Differences'''.
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||05:19
||The same two options appear for '''T Estimate'''.

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||05:24
||'''Difference of Means''' is for '''unpaired T Test'''.

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||05:29
||'''Paired Differences''' is for '''paired T Test'''.
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||05:34
||The '''T Test''' compares two groups at a time.
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||05:38
||Select '''T Test: Difference of Means'''.
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|| 05:42
||'''Column A''' data are denoted by default as '''Sample 1'''.

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||05:48
||'''Column B''' data are denoted by default as '''Sample 2'''
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||05:54
||Click on the '''menu buttons''' next to the displays to reverse the order.

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||06:02
||As Mean of '''column B''' is greater than Mean of '''column A''', '''T values''' and '''limits''' will now be positive.
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||06:14
||'''T Tests''' give '''t''' and '''P''' values.

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||06:19
||Comparing '''A''' and '''B''' gives '''P''' less than 0.001 and '''T value''' greater than 4.

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||06:29
||Thus, feeds '''A''' and '''B''' have a significant effect on lengths of fish.
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||06:37
||Click on the '''menu button''' and choose '''T estimates, Difference of Means'''.
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||06:45
||'''T Estimates''' give '''lower''' and '''upper limits''' for the '''Mean Difference'''.

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||06:51
||The '''confidence level''' is 95%.

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||06:55
||We can be 95% sure that the '''Mean difference''' is between the '''lower''' and '''upper limits'''.

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||07:04
||Close the '''Data Analysis window'''.
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||07:07
||Now let us look at the '''Probability Calculator'''.
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||07:12
||We are in the '''Spreadsheet''' view.

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||07:15
||Use the '''mouse''' to drag and highlight length data for '''feed A'''.
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||07:22
||Click on '''One Variable Analysis''' tool.

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||07:27
||In the '''Data Source''' popup window that appears, click on '''Analyze''' button.
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||07:33
||At the top of the '''Data Analysis''' window, click on the second( 2nd) '''Show Statistics''' button.

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||07:41
||Note down '''Mean mu (µ)''' and '''Standard deviation sigma (σ)'''.
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||07:49
||Close the '''Data Analysis''' window and follow the same steps for '''feed B'''.
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||07:57
||Again, drag and highlight '''feed A''' length data.
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||08:02
||Click on '''View''' and then click on '''Probability Calculator'''.
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|| 08:08
||The '''Probability Calculator''' window pops up.
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||08:12
||Drag the boundary to see it properly.
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||08:16
||We are looking at a '''normal distribution''' in the '''Distribution''' window.
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|| 08:22
||Place your '''cursor''' on the horizontal boundary below the '''distribution curve'''.

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||08:28
||Drag the arrow upwards to see the data entry window below the '''curve''' properly.
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||08:36
||Let us look at a '''normal distribution''' for fish given feed '''A'''.
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|| 08:42
||In the box next to '''mu (μ)''', type 745.5 and press '''Enter'''.
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||08:51
||In the box next to '''sigma (σ)''', type 29.0215 and press '''Enter'''.
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||09:01
||A '''normal distribution''' plot appears with mean 745.5 and '''sigma''' 29.0215.
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||09:13
||Click on the 1<sup>st</sup> of three buttons below the '''Mean''' and '''σ''' boxes.
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||09:20
||The right side bracket indicates, this is the upper limit.
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||09:25
||In the box next to '''P of X''' less than or equal to, type 770 and press '''Enter'''.
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||09:35
||Note that the '''probability P''' appears in the box to the right, 0.8007.

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||09:44
||Thus, 80.07% fish fed feed '''A''' are 770 milimeters long or shorter.
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||09:55
||Let us do the reverse.

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||09:58
||In the '''P''' box to the right of the equal to sign, type 0.09.

Press '''Enter'''.
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||10:08
||When you press '''Enter''', '''X''' less than or equal to 706.5893 appears in the box.
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||10:17
||Thus, 9% of the fish are shorter than this length.
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||10:23
||Next to the '''Normal''' display box, click on the '''curve symbol'''.
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||10:28
||The '''cumulative distribution function curve''' appears.
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||10:33
||'''Probability''' is plotted on the '''y axis''', length of '''feed A''' group is plotted on '''x axis'''.
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||10:43
||Click on '''curve symbol''' to return to the '''normal distribution bell curve'''.
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||10:50
||Below '''mu''' and '''sigma''' displays, click on 2nd of the three buttons.
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||10:57
||The two brackets indicate that lower and upper limits can be specified.
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||11:04
||In the first box, type 705 and in the second box, 758, press '''Enter'''.
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||11:14
||'''P''' equal to 0.5852 appears.

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||11:20
||This means 58.52% of fish fed '''feed A''' are 705 to 758 milimeter long.
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||11:32
||Finally, click on the 3<sup>rd</sup> button showing a left bracket.
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||11:38
||In the box, type 760 and press '''Enter'''.
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||11:45
||30.87% of fish fed '''feed A''' are longer than 760 mm.
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||11:54
||Next to '''Distribution''' tab, click on '''Statistics''' tab.
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||11:59
||Close the '''Probability Calculator''' window.
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|| 12:03
||Let us look at the '''Spreadsheet''' in '''GeoGebra'''.
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||12:08
||Use '''mouse''' to drag and highlight length data in '''columns A''' and '''B'''.
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||12:16
||Under '''One Variable Analysis''', select '''Probability Calculator'''.
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||12:22
||We are looking, as before, at the '''Statistics''' window.
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||12:27
||From the dropdown menu at the top, select '''T Test, Difference of Means'''.
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||12:34
||You can type '''mean, standard deviation σ''' and total number of samples '''N''' in the boxes.

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||12:43
||We will type 10 for '''N''' as each feed group has 10 fish.

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||12:50
||Press '''Enter''' after entering all values.
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||12:54
||'''Feed A''' Mean is lower than '''feed B''' Mean.
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||13:00
||So we will choose '''feed B''' group as '''Sample 1''' and '''feed A''' as '''Sample 2'''.

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||13:08
||Note '''t''', standard error, degrees of freedom and '''P''' values.

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||13:15
||Compare them to results from '''Multiple Variable Analysis'''.

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||13:21
||Select different tests for different pairs of columns in the '''Spreadsheet'''.

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||13:27
||Interpret the results and compare with your calculations.
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||13:33
||Let us summarize.
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||13:35
||In this '''tutorial''', we have learnt how to use '''Probability Calculator''' in '''GeoGebra'''.

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||13:43
||Looked at different '''distributions''' and '''parameters'''.
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||13:48
||Assignment

Perform statistical analyses for weight and girth data given in this '''tutorial'''.

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||13:57
||Four oils were used to deep fry chips.

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||14:02
||Amount of absorbed fat was measured for six chips fried in the four oils.

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||14:10
||Is any of the oils absorbed more than the others?

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||14:16
||The video at the following link summarizes the '''Spoken Tutorial project'''.

Please download and watch it.
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||14:25
||The '''Spoken Tutorial Project''' team conducts workshops and gives certificates.

For more details, please write to us.
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||14:35
||Please post your timed queries on this forum.
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||14:39
||'''Spoken Tutorial Project''' is funded by NMEICT, MHRD, Government of India.

More information on this mission is available at this link.
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||14:52
||This is '''Vidhya Iyer''' from '''IIT Bombay''', signing off.

Thank you for joining.
|-
|}

Applications-of-GeoGebra/C3/Probability-and-Distributions/English-timed - Revision history

PoojaMoolya: Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- ||00:01 ||Welcome to this '''tutorial''' on '''Probability and Distributions in GeoGebra'''. |- ||00:08 ||In this '''tutorial''',..."