A random variable X has a distribution function given by: (0, F(x)= {k(x-1)*, 13 1. Determine the value of k. 2. Find its corresponding probability density function.

The probability density function

The probability density function for a continuous random variable X is given by 0 < x < 1 1≤ x ≤ 2 else Find P(0.5 < X < 1.5) Round to 4 decimal places if needed. f(x) = X 2-x

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.