A continuous random variable X has probability density function (pdf): f(x) = {31:2, 0 S x E 1 0, elsewhere (a) Verify that x) is a proper pdf. (2 marks) Note: There are 2 requirementsfoonditions. (b) Find the probability PtX ~= Vi ). (2 marks} (c) Find the cumulative distribution function (cdf) F(x). (2 marks) Note: You must give F(x) for all real values of x from 00 to +00. (d) Find the expectation ELK) of X. (2 marks}