In: Statistics and Probability
2 Consider the probability density function (p.d.f) of a continuous random variable X: f(x) = ( k x3 , 0 < x < 1, 0, elsewhere, where k is a constant. (a) Find k. (b) Compute the cumulative distribution function F(x) of X. (c) Evaluate P(0.1 < X < 0.8). (d) Compute µX = E(X) and σX.