F(x)=0.25x+0.5 x < -2 -2≤x<2 25x Determine the probability that the random variable X is greater than -1.

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

Weights (X) of men in a certain age group have a normal distribution with mean ? = 170 pounds and standard deviation ? = 28 pounds. Find each of the following probabilities. (Round all answers to four decimal places.) (a) P(X ≤ 191) = probability the weight of a randomly selected man is less than or equal to 191 pounds. (b) P(X ≤ 156) = probability the weight of a randomly selected man is less than or equal to 156 pounds. (c) P(X > 156) = probability the weight of a randomly selected man is more than 156 pounds

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)?

For each random variable defined, describe the set of possible values for the variable, and state whether the variable is discrete or continuous.  (a) U = number of times a surfer has to paddle in front of a wave before catching one (b) X = length of a randomly selected angelfish

The table shows the results of a restaurant survey. Find the probability P(Y'IC'). Service Great Meal Lunch (X) Dinner (Y) Total 4247 (A) Service Good (B) Service Okay (C) Service Poor Total (D) 32 47 14 45 45 47 14 43 77 94 28 88 80 138 149 287 P(Y'|C')= (Simplify your answer. Type an integer or a simplified fraction.)