Question

In: Statistics and Probability

Sarah D's road manager plays a dice game with two dice. The six sides of on...

Sarah D's road manager plays a dice game with two dice. The six sides of on each die are numbered from 2 to 7. Define the random variable X to be the sum of the numbers on the up-face of the two dice when rolled.

a. Construct table showing PDF and the CDF of the random variable X

b. Calculate the mode of the distribution.

c. Calculate the expected value of X.

d. Calculate variance of X.

e. Calculate P(4

Expert Solution

a) The PDF of the random variable is constructed below.

X	4	5	6	7	8	9	10	11	12	13	14
P(X=x)	1/36	2/36	3/36	4/36	5/36	6/36	5/36	4/36	3/36	2/36	1/36

The CDF of the random variable is constructed below.

X	4	5	6	7	8	9	10	11	12	13	14
P(X<=x)	1/36	3/36	6/36	10/36	15/36	21/36	26/36	30/36	33/36	35/36	36/36=1

b) The mode of the distribution is the value of which has the largest probability of occurring. See the PDF table.

The mode is with probability 6/36 = 1/6.

c) The expected value is

d) The variance is calculated as

orchestra answered 2 years ago

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