1. Let X be a continuous random variable, with the pdf (probability density function), fx(x) = 6x(1-x) 0

1. Let X be a continuous random variable, with the pdf (probability density function), fx(x) elsewhere (a) (5 pts) Find the expected value E (b) (10 pts) Find the variance Var[X] . (c) (10 pts) If X is a continuous random variable, show that ElaX + b] = a E[XJ + b where a and b are (d) (5 pts)Find E[6X + 10 xz + 5]. (e) (10 pts) Using the Markov's inequality, show that, P ( X 2 2