Indicators:

Let A be an event, and let IA be the associated indicator random variable: IA (w) = 1 if w belongs A, and IA (w) = 0 if w doesn't belong to A.

Similarly, let IB be the indicator of another event, B. Suppose that, P (A) = p, P (B) = q, and P (A union B) = r.

1. Find E [(IA - IB)²] in terms of p, q, r.

2. Determine Var (IA-IB) in terms of p, q, r.

Attachment:

Indicators Let A be an event, and let IA be the associated indicator random variable: IA (w) = 1 if we A, and IA (w) = 0ifwe A. Similarly, let Is be the indicator of another event, B. Suppose that, P (A) = p, P (B) = q, and P (A U B) = r. 1. Find E [(IA - IB )"] in terms of p, q, r. 2. Determine Var (IA - IB ) in terms of p, q, r