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
![](https://test.transtutors.com/qimg/33052093-225d-4666-bf10-2640be13de58.png)
(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
![](https://test.transtutors.com/qimg/8e106c7e-bc40-4bcd-8896-821a0d7c33c0.png)