Q1) Assume that probability distribution of random variable x can be explained by formula

P(X) =   X / 15    For each of the values X= 1,2,3,4 and 5

For example, then, p(X=2)=p(2)=2/15

a) Write out probability distribution of X.

b) Illustrate that probability distribution of X satisfies properties of a discrete probability distribution.

c) Compute mean of X.

d) Compute variance,  σ²_x and the standard deviation σ_x

2) John and Jasmine are married. Probability that john watches certain television show is .4. Probability that Jasmine watches show is .5. Probability that john watches show, given that Jane does is .7.

a) Determine the probability that both john and Jasmine watch the show.

b) Determine the probability that Jasmine watches show, given that john does.

c) Do john and Jasmine watch the show independently of each other? give explanation for your answer.