5. [3] The life expectancy (in years) for a particular brand of microwave oven is a continuous random variable with the probability density function below. Find d such that the probability of a randomly selected microwave oven lasting d years or less is 0.5. if x ≥ 0 f(x) = f(x) = 4 (x+4)²' 0 J otherwise

5. Let X be a positive random variable; i.e., P(X - log(EX) (b) E[log(1/X)] > log[1/EX] (c) E (X³) > (EX)³

A continuous random variable, X, has the following probability density function. k cos for 0sxs1 f(x)=- for all other values of x (a) Show that k = Find p( x sxs). (b) (c) Find the median of X.