10. [9 marks] When a conventional paging system transmits a message, the probability that the message will be received by the appropriate pager is p. To be confident that a message is received at least once, a system transmits the message n times. (a) Assuming all transmissions are independent, what is the PMF of K, the number of times the pager receives the same message? (b) Assume p=0.7. What is the minimum value of n that produces a probability of 0.95% of receiving the message at least once? (c) Assume p = 0.7. Assume also that a successful transmission costs $2.00 and an unsuccessful one costs $0.25. The cost of a page Y is then a random variable. Describe the sample space and find PMF of Y. 11. [10 marks] The PMF of the random variable X is given by (a) The value of a is? k = 0 k = 1 Px[k] = = k=2 a k=3 0 otherwise (b) Calculate the second moment of X, E(X). (c) Calculate the Variance of X. (d) Calculate the value of the CDF of X evaluated at x = 2.5. (e) Find the probability that the random variable Y = X2+1 is less than or equal to 3.0.