Let x a be the indicator random variable for event a with

Question

Let X A be the indicator random variable for event A with probability P[A] = 0.8. Let _n(A) denote the relative frequency of event A in n independent trials.

(a) Find E[X A] and Var[XA].

(b) What is Var[_n(A)]?

(c) Use the Chebyshev inequality to find the confidence coefficient 1 - α such that ₁₀₀(A) is within 0.1 of P[A]. In other words, find α such that

(d) Use the Chebyshev inequality to find out how many samples n are necessary to have _n(A) within 0.1 of P[A] with confidence coefficient 0.95. In other words, find n such that