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andom variable X has the binomial distribution with probability Function P(X = z) = (²) p² (1 − p)²-², = 0, 1, 2 and 0

andom variable X has the binomial distribution with probability Function P(X = z) = (²) p² (1 − p)²-², = 0, 1, 2 and 0

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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5. The random variable X has the binomial distribution with probability mass function P(X = z) = (²)p²(1 − p)²¹¹, z = 0.1,2 and 0<p<1. That is, X Bin(2.p) 2 Let Y = X₁ + X₂ +...+X100 be the sum of 100 independent random variables, each distributed as X. (a) Explain why the random variable has Bin (200, p) distribution. 2 (b) Using a suitable approximation, find P(Y> 140) when p 3 (c) Using a suitable approximation, find P(Y> 2) when p = 0.02.
Transcribed Image Text:5. The random variable X has the binomial distribution with probability mass function P(X = z) = (²)p²(1 − p)²¹¹, z = 0.1,2 and 0<p<1. That is, X Bin(2.p) 2 Let Y = X₁ + X₂ +...+X100 be the sum of 100 independent random variables, each distributed as X. (a) Explain why the random variable has Bin (200, p) distribution. 2 (b) Using a suitable approximation, find P(Y> 140) when p 3 (c) Using a suitable approximation, find P(Y> 2) when p = 0.02.
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