Chapter Probability

Please help me with working steps on probability

QUESTION 5 a) Give TWO (2) characteristics of discrete random variable. (2 marks) b) A book seller sells a special educational book package that consists of five books per package. A customer can purchase the whole set of five books or each book individually. The probability distribution of Y, the number of books purchase from each package, is given as follow. Y=y m 4 5 P ( Y = y) 0.45 0.15 0. 15 0.25i} ii) iii) |Given that E(Y) = 2.?5, nd the values of m. (3 marks) Find the probability that a customer purchase at most four books. (2 marks] Calculate E (Y2 21" + 2). (4 marks) Suppose that X is a continuous random variable that represent the customers' waiting time (in minutes) after getting a queue number at post office. The probability density function is given as follows: 1'2 + 3 fix) = 24 [J elsewhere 11:154- Show that s = '1. (3 marks) Find that the customer's waiting time after getting a queue number at post office is not less than 1.5 minutes. (3 marks) Calculate E(X2]. (4 marks) 95 Find the standard deviation ofXgiven that E(X) = E . (2 marks] 3 Find the total variance ofX and Y, if the variance of Y is E . (2 marks)