Consider dice that are tetrahedral in shape with the corners of each die labeled

Question

Consider dice that are tetrahedral in shape with the corners of each die labeled with the numbers 1,2,3,4. When a pair of these die are tossed, let the random variable associated with each outcome be the products of the two numbers at the top of the dice if the product is odd otherwise x=0.

a. Setup a sample SPace table, along with the associated value of the random variable x.

b. Determine the probability associated with each different value of Xi, i.e. p(xi).

c. Compute the average value of X. i.e. < x > = Sum Xi P(Xi)

d.Compute the variance.

e. Compute the Standard deviation

Explanation / Answer

a) the values of random variable = 0, 1 and 9

b) probablity of x= 1

when both die have the corner marked 1 up= 1/4 X 1/4

= 1/16

probablity of x= 9

when both die have the corner marked 3 up= 1/4 X 1/4

= 1/16

probablity of zero = 1- ( probablity of 1 + probablity of 9)

= 7/8 = 0.875

c) average value of X = 1 X 1/16 + 9X1/16 + 0 X 1/16

= 5/8 = 0.625

d) variance = (1^2- 0.625) X 1/16 + (9^2 - 0.625) X 1/16 + 0

= 0.553125 = 177/320

e) standard deviation = root of variance = 0.74372

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