The number of claims on an insurance policy is a random variable with the following CDF: x< 0 0.62, 0

Let X be a random variable that can take values x = 2,4,6,8 and has probabilities given by the function P(X = x) = 3x/60 Find (1) P(X = 4) (2) P (X ≤ 6) (3) P(X < 6) (4) P (X ≥ 3)

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)?

The random variable x is N(10,1). Find f(x(x-10)²<4).

3 The median value y of a continuous random variable is that value such that F(y) = 0.5. Find the median value of the random variable in 90.5 = f(y) = 2 25 -Y, 0 ≤ y ≤ 5, elsewhere. 0,

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