Let X be a continuous random variable whose distribution has a probability density function (PDF) cx\

Let X be a continuous random variable whose distribution has a probability density function (PDF) cxk, for x e (O, I), f(x) = o, for x (O, I). Here c is a real number, and k is a real number greater than I. Please answer the following questions. I. 2. 3. 4. 5. What is the value of c so that f(x) is a valid PDF? Find the cumulative distribution function (CDF) of the random variable X. Let O a < b I. Derive a formula for P(a < X < b). Let > O and > O. Find the expectation E(5X'Il 2Y2). Let > O and > O. Find the expectation 2Y2).