# Two dice are thrown simultaneously 25 times. The following price of observation are obtained.(2, 3) (2, 5) (5, 5) (4, 5) (6, 4) (3, 2) (5, 2) (4, 1) (2, 5) (6, 1) (3, 1) (3, 3) (4, 3) (4, 5) (2, 5) - Mathematics and Statistics

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Sum

Two dice are thrown simultaneously 25 times. The following price of observation are obtained.
(2, 3) (2, 5) (5, 5) (4, 5) (6, 4) (3, 2) (5, 2) (4, 1) (2, 5) (6, 1) (3, 1) (3, 3) (4, 3) (4, 5) (2, 5) (3, 4) (2, 5) (3, 4) (2, 5) (4, 3) (5, 2) (4, 5) (4, 3) (2, 3) (4, 1)
Prepare a bivariate frequency distribution table for the above data. Also, obtain the marginal distributions.

#### Solution

Let X = Observation on 1st die
Y = Observation on 2nd die
Now, minimum value of X is 1 and maximum value is 6.
Also, minimum value of Y is 1 and maximum value is 6.
Bivariate frequency distribution can be prepared by taking X as row and Y as column.
Bivariate frequency distribution is as follows:

 Y/X 1 2 3 4 5 6 Total (fy) 1 – – I II – I 4 2 – – I – II – 3 3 – II I III – – 6 4 – – II – – I 3 5 – IIII – III I – 9 6 – – – – – – 0 Total (fx) 0 7 5 8 3 2 25

Marginal frequency distribution of X:

 X 1 2 3 4 5 6 Total Frequency 0 7 5 8 3 2 25

Marginal frequency distribution of Y:

 Y 1 2 3 4 5 6 Total Frequency 4 3 6 3 9 0 25
Is there an error in this question or solution?
Chapter 4: Bivariate Frequency Distribution and Chi Square Statistic - Exercise 4.1 [Page 49]

#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 4 Bivariate Frequency Distribution and Chi Square Statistic
Exercise 4.1 | Q 2 | Page 49

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