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Let x be a... a) Let x be a discrete random variable such that: P(x) = C(n, x) p² (1 – p)"-² for all 0 < x < n, x E Z. Show that when p is small, and n is really, REALLY large, that P(x) = where X= np. x! ed' Hint: when n is really, REALLY large, e" (1+ 2)". b) Let x be a discrete random variable such that:

Let x be a... a) Let x be a discrete random variable such that: P(x) = C(n, x) p² (1 – p)"-² for all 0 < x < n, x E Z. Show that when p is small, and n is really, REALLY large, that P(x) = where X= np. x! ed' Hint: when n is really, REALLY large, e" (1+ 2)". b) Let x be a discrete random variable such that:

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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Need to prove the following:

Let x be a... a) Let x be a discrete random variable such that: P(x) = C(n, x) p* (1 – p)"- for all 0 < x < n, x E Z. n-x Show that when p is small, and n is really, REALLY large, that where X= np. P(x) 2 Hint: when n is really, REALLY large, eª 2 (1+ 2)". x! ed' b) Let x be a discrete random variable such that: P(x) for all x > 0, εΖ. x! ed Use the fact that e to show that the expected value x= of x is equal to A. c) Let x be a discrete random variable with expected value u. Show that (x – H)² = x(x – 1) + x – 2xµ + µ². d) Let x be a discrete random variable such that: P(x) = x! e for all x > 0, x E Z. Use the fact that e and that (x – µ)² = x(x – 1) +x – x! x=0 2.xu + µ? to show that the variance of x is equal to the expected value of x.
Transcribed Image Text:Let x be a... a) Let x be a discrete random variable such that: P(x) = C(n, x) p* (1 – p)"- for all 0 < x < n, x E Z. n-x Show that when p is small, and n is really, REALLY large, that where X= np. P(x) 2 Hint: when n is really, REALLY large, eª 2 (1+ 2)". x! ed' b) Let x be a discrete random variable such that: P(x) for all x > 0, εΖ. x! ed Use the fact that e to show that the expected value x= of x is equal to A. c) Let x be a discrete random variable with expected value u. Show that (x – H)² = x(x – 1) + x – 2xµ + µ². d) Let x be a discrete random variable such that: P(x) = x! e for all x > 0, x E Z. Use the fact that e and that (x – µ)² = x(x – 1) +x – x! x=0 2.xu + µ? to show that the variance of x is equal to the expected value of x.
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