Please answer the first question, if possible the second question as well.

1.2 Proofs 1. The variance of a discrete random variable X is defined as: 02 = [(x - 1)2f(2) Alternatively, you can use 82 = [x2 f(x) - 12 Show that these two expressions for of are equal. Hints: Remember that Ex f(x) = 1 and / = Exxf(x) 2. Suppose X is a Bernoulli random variable with parameter p. Find the variance of X. Check that the two methods given in 1.2.1 computing the variance give the same