(a) Suppose that X is a continuous random variable with a probability density function: f(x)={C(4x−2x2)0​01). (b) Let X be a random variable. X has the following probability distribution: xP(X=x)​−11/5​02/5​12/5​​ What is the probability distribution of W=X2 ? (c) The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by f(x)={x210​0​x≥10x≤10​ i) Determine the cumulative distribution function of X. ii) Determine the mode (point of maximum density), and the median ( m such that P(X≤m)=F(m)=0.5).