Probstat/week5 practice 2

This is part of probstat.

Independent random variables

1. Consider a simple experiment of choosing, uniformly at random, an integer from the set {0,1}.

• 1.1 Let X be a random variable that denotes the chosen integer from the experiment. Find E[X] and Var(X).
• 1.2 Let's perform the experiment 2 times. Let X₁ and X₂ that denote the chosen integers from the first and the second experiments. Let Y = (X₁ + X₂)/2. Find E[Y] and Var(Y).