Question: 2. The random variable X has the following probability density function: where c is a constant. ct -1 t , 2; f (t) =

2. The random variable X has the following probability density function: where c is a constant. ct -1 t , 2; f (t) = otherwise, (a) Find the constant c. Sketch the pdf and cdf of X. (b) Find E(X) and Var (X). (c) Suppose Y = 2 X. What is the range of Y? Find the density function fy (t) of Y. Remark: Notice the function g(x) = x is not monotone on the interval [1,2]. (d) Find E(X2) using the density fy (t).

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