Show that for any random variable E[X2]≥ (E[X])² and When does one have equality?

der a random sample X1, X2, ..., X, having the pdf, f(r; 0) 1

A fair coin is tossed three times. The random variable X is defined to be , where h is the number of flips that come up heads. For example, X(HHT) = 2 . What is E[X]?

Let X be a random variable that can take three values: -1, 0 , 1, and let Mx(t) be the moment generating function(MGF) of X. Assume that Mx(t) 1 for any -0