Question 2: Let X be a continuous random variable with the following probability density function 312 -15150 otherwise (a) [3 pts] Check if f(x) is a legitimate probability density function. Show steps. (b) [2 pts] Calculate the probability P(X = 0.5)? (c) [2pts] Calculate the expected value E(X). (d) [3pts] Let Y = 2X. Find the 87.5th percentile of Y