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Hint: Let p = x+y 4.10. Let X be a binomial random variable with parameters n and p. Show that 1 1-(1-p)"+¹ (n + 1)p 4.11. Let X be the number of successes that result from 2n independent trials,

Hint: Let p = x+y 4.10. Let X be a binomial random variable with parameters n and p. Show that 1 1-(1-p)"+¹ (n + 1)p 4.11. Let X be the number of successes that result from 2n independent trials,

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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How to solve that question 4.10?

**Hint:** Let \( p = \frac{x}{x+y} \). **4.10.** Let \( X \) be a binomial random variable with parameters \( n \) and \( p \). Show that \[ E \left[ \frac{1}{X+1} \right] = \frac{1 - (1-p)^{n+1}}{(n+1)p} \] **4.11.** Let \( X \) be the number of successes that result from \( 2n \) independent trials.
Transcribed Image Text:**Hint:** Let \( p = \frac{x}{x+y} \). **4.10.** Let \( X \) be a binomial random variable with parameters \( n \) and \( p \). Show that \[ E \left[ \frac{1}{X+1} \right] = \frac{1 - (1-p)^{n+1}}{(n+1)p} \] **4.11.** Let \( X \) be the number of successes that result from \( 2n \) independent trials.
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Could you explain what was done in more detail, starting from the "or" on step 3, where we have a multiplication [1/(n+1)p] outside the summation? Where did this [1/(n+1)p] come from, and so on?

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