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Find the expected value of q. d. Let X1, X2,., Xn be i.i.d. Bernoulli(p). Suppose q =

Find the expected value of q. d. Let X1, X2,., Xn be i.i.d. Bernoulli(p). Suppose q =

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Transcription:** Let \(X_1, X_2, \ldots, X_n\) be i.i.d. Bernoulli(\(p\)). Suppose \(q = \left(\frac{\sum_{i=1}^{n} X_i}{n}\right)^2\). Find the expected value of \(q\). **Explanation:** This question is from a probability and statistics context. It details a sequence of independent and identically distributed (i.i.d.) random variables \(X_1, X_2, \ldots, X_n\), each following a Bernoulli distribution with parameter \(p\). The variable \(q\) is defined as the square of the average of these Bernoulli variables. The task is to find the expected value (mean) of this variable \(q\).
Transcribed Image Text:**Transcription:** Let \(X_1, X_2, \ldots, X_n\) be i.i.d. Bernoulli(\(p\)). Suppose \(q = \left(\frac{\sum_{i=1}^{n} X_i}{n}\right)^2\). Find the expected value of \(q\). **Explanation:** This question is from a probability and statistics context. It details a sequence of independent and identically distributed (i.i.d.) random variables \(X_1, X_2, \ldots, X_n\), each following a Bernoulli distribution with parameter \(p\). The variable \(q\) is defined as the square of the average of these Bernoulli variables. The task is to find the expected value (mean) of this variable \(q\).
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Bernoulli Trail: In probability theory, a Bernoulli trial is a random experiment which has exactly two possible outcomes viz. Success and Failure. In Bernoulli trails, the probability of success remains same every time the experiment is conducted.

If X is a random variable denoting the Bernoulli distribution, then the probability mass function of X is given by,

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