Stats problems need done ASAP

Problem 1.

(A)

a. px (X) = 1/6; y =

(B)

(C)

Problem 2.

(A)

(B)

(C)

Problem 3.

(A)

(B)

Problem 4.

(A)

(B)

(C)

Problem 5.

(20pts) A fair coin is independently tossed three times until a head appears,

whichever comes first. Let X denotes the number of heads.

(A) Write the sample space with associated probabilities for outcomes,

and then find the probability distribution of X.

(B) What is the expected number of heads.

Problem 6.

(20pts) A fair coin is independently tossed three times until a head appears,

whichever comes first. Let X denotes the number of tails.

(A) Write the sample space with associated probabilities for outcomes,

and then find the probability distribution of X.

(B) What is the expected number of tails.