You are given the following cumulative density function. Find the probability density function as a piecewise function.

Let X be a continuous random variables with with the following probability density function.Answer the following questions.Find the value of α such that f(x) is a probability density function. Make sure thatyou show all the steps.Find the cumulative distribution function of X. Show it on a graph. Make sure thatyou show all the steps.Find the expected value and variance of X. Make sure that you show all the steps.Find the probability density function of Y = X2. Make sure that you show all thesteps.

The graph shows the uniform density function for a friend who is x minutes late. Find the probability that the friend is at least 15 minutes late.

Find k such that the function is a probability density function over the given interval. Then write the probability density function. f(x) = kx, 1≤x≤8 What is the value of k? k = 1 (Simplify your answer.) What is the probability density function? f(x) =