How many time do we need to run the experiment

Assignment Help Basic Statistics

Reference no: EM131216262

Suppose we wish to estimate the probability,P_A, of some event, A. We do so by repeating an experiment times and observing whether or not the event occurs during each experiment. In particular, let

(a) Assuming n is large enough so that the central limit theorem applies, find an expression for

(b) Suppose we want to be 95% certain that our estimate is within of the true value. That is, we want How large does need to be? In other words, how many time do we need to run the experiment?

(c) Let be the number of times that we observe the event during our repetitions of the experiment. That is Assuming that is chosen according to the results of part (b), find an expression for the average number of times the event is observed Show that for rare events is essential independent of P_A . Thus, even if we have no idea about the true value of P_A , we can run the experiment until we observe the event for a predetermined number of times and be assured of a certain degree of accuracy in our estimate of pA.

Reference no: EM131216262

Questions Cloud

Draw the histogram and the density of the simulated values : Simulate 10000 values of (Y - µ)'∑-(Y - µ), where ∑- is a g-inverse for the covariance of Y. Find the mean and variance of the simulated values. Also draw the histogram and the density of the simulated values

Find a bound to the probability using markovs inequality : Find a bound to the probability using Markov's inequality. - Find a bound to the probability using Chebyshev's inequality.

Calculate the payback period for each of the investments : Calculate the payback period for each of the investments. If the maximum acceptable payback period is 3 years, which of the investments would be accepted?

Do you perceive an ethical dilemma : You are in your second year as an auditor with Dantly and Regis, a regional CPA firm. One of the firm's long-time clients is Mayberry-Cleaver Industries, a national company involved in the manufacturing, marketing, and sales of hydraulic devices used..

How many time do we need to run the experiment : How large does need to be? In other words, how many time do we need to run the experiment?- find an expression for the average number of times the event is observed.

Briefly relate the strategic twists of this story correctly : Can you briefly relate the strategic twists of this story correctly, not the whole thing? It has interesting nuances and twists - What is being kept secret here? Who is actually hiding something here, if anyone?

Contrast the cost method and the par value method : Accounting for Treasury Stocks For numerous reasons, a corporation may reacquire shares of its own capital stock. When a company purchases treasury stock, it has two options as to how to account for the shares: the cost method and the par value metho..

Describing the concept of nature versus nurture : Using your own words, write 175 to 350 words describing the concept of "nature versus nurture." Be sure to explain how nature, nurture, and both concepts are involved in development.

Discuss the actuarial funding methods-pension bene?ts : Pension Bene?ts Pension accounting has become more closely associated with the method of deter-mining pension bene?ts. Discuss the following methods of determining pension bene?ts: Discuss the following actuarial funding methods:

User Account

All Pages