7. A discrete random variable X taking non-negative integer values has probability gen- erating function: rx(t) = =0F 1 %3D (2 - t)2 Calculate Var(X).

7. A discrete random variable X taking non-negative integer values has probability gen- erating function: 1 rx(t) = (2- t)2 (a) Calculate P(X = 2).

Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)

#2: Suppose a random variable X has expected value E[X] = 3 and variance Var(X) = 4. Compute the following quantities. (a) E[3X + 2] (b) E[X²] (c) E[(3X+2)²] (d) Var[2X + 2]

Z is the present-value random variable for a whole life insurance of b payable at the moment of death of (x). You are given: (i) (ii) 8 = 0.05 (iii) The net single premium for this insurance is equal to Var(Z). Calculate b. x+t = 0.01 t≥0 (A) 1.36 (B) 1.68 (C) 2.00 (D) 2.32 (E) 2.64

Suppose that a medical test has a 85% chance of detecting a disease if the person has it (P(PT|D)=0.85) and a 90% chance of correctly indicating that the disease is absent if the person really does not have the disease (P(NT|Dc=0.90). Suppose that 95% of the population does not have the disease P(Dc)=0.95  What is the probability that a randomly chosen person will test negative P(NT)?