Question

A game consists of first rolling an ordinary six-sided die once and then tossing an unbiased coin once. The score, which consists of adding the number of dots showing on the die, and the number of heads showing on the coin (0 or 1), is a random variable, say X.

a) List the possible values of X, and write its PMF in the form of a table.

b) Draw a graph of the PMF.

c) What is the CDF of X? Write it in the form of a table.

d) Draw a graph of the CDF of X. e) Find P[X > 3].

f) Find the probability that the score is an odd integer.

Answer 1

a)

b)

c)

d)

e)

P(X>3) = P(X=4)+P(X=5)+P(X=6)+P(X=7)

= 0.17 +0.17+0.17 +0.08

= 0.59 Answer

f)

P(X=ODD) = P(X=1)+P(X=3)+P(X=5)+P(X=7)

= 0.08 + 0.17 +0.17 + 0.08

= 0.5 Answer