# Question: Suppose we wish to estimate the probability PA of some

Suppose we wish to estimate the probability, PA, of some event A as outlined .As motivated by the result, suppose we repeat our experiment for a random number of trials, N. In particular, we run the experiment until we observe the event A exactly m times and then form the estimate of PA according to

Here, the random variable represents the number of trials until the m th occurrence of A.

(a) Find E [ṔA]. Is this estimate unbiased?

(b) Would it be better to use ṔA = m / N as an estimate?

Here, the random variable represents the number of trials until the m th occurrence of A.

(a) Find E [ṔA]. Is this estimate unbiased?

(b) Would it be better to use ṔA = m / N as an estimate?

**View Solution:**## Answer to relevant Questions

The noise level in a room is measured n times. The error Ɛ for each measurement is independent of the others and is normally distributed with zero- mean and standard deviation σe = 0.1. In terms of the true mean, μ, ...A node in a communication network receives data packets of variable length. Each packet has a random number of bits that is uniformly distributed over the integers {100, 101, 102… 999}. The number of packet arrivals per ...Let X be a zero- mean, unit- variance, Gaussian random variable and let Y be a chi- square random variable with n–1 degrees of freedom (see Appendix D, section D. 1.4). If X and Y are independent, find the PDF of One way ...A wide sense stationary, discrete random process, X [n] , has an autocorrelation function of . RXX [k] Find the expected value of Y[n] =(X [n+ m] – X [n– m]) 2, where is an arbitrary integer. Two zero- mean discrete- time random processes, X [n] and Y [n], are statistically independent. Let a new random process be Z [n] = X [n] + Y [n]. Let the autocorrelation functions for X [n] and X [n] be Find RZZ [k]. Plot ...Post your question