1. 10 multiple choicequestions each of which has 5 choices. John decides to choose answers randomly for this test. using R for right and W for wrong indicating if John gets the question right or wrong.

a) random variable X represents the total number of right answers. What isthe distribution of X and specify the values of its parameters? b) Use y(W,W,W,R,W,R,R,W,R,R)=4to representJohn getting the first three questions wrong and then the fourth being correct. find the probability P(y=4)

c)derive a PMF for y and prove it is valid.

2. Vancouver was hit by an average of 4 storms on average per year. The actual number of storms follows a Poisson distribution. what's the probability that Vancouver will have 5 or more storms in next year?