Answer 4 and 5 if possible

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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Answer 4 and 5 if possible

 

**Transcription for Educational Website:**

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**(4)** If \( X \) is a geometric random variable \( \text{Geometric}(p) \), i.e., \( P(X=k) = p(1-p)^k, k=0,1,2,\ldots \), then \( E(X) \) is

- [ ] \( \frac{1}{p} \) ◉
- [ ] 0
- [ ] \( p \)
- [ ] \( (1/p)-1 \)
- [ ] \( (1/p)+1 \)
- [ ] N/A

**(5)** If \( X \) is a normal \( N(0,1) \) random variable then \( E(X) \) is

- [ ] 0 ◉
- [ ] 1
- [ ] -1
- [ ] \( +\infty \)
- [ ] \(-\infty \)
- [ ] N/A

**(6)** Find the variance of \( X \) when \( X \sim \text{Geometric}(p) \).

The correct answer is

- [ ] \( \frac{1-p}{p^2} \) ◉
- [ ] \( \frac{1}{p^2} \)
- [ ] \( \frac{1}{p} \)
- [ ] \( \frac{1}{p} - 1 \)
- [ ] None of the above
- [ ] N/A

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Each question provides a multiple-choice format where the correct response is marked with a filled circle (◉).
Transcribed Image Text:**Transcription for Educational Website:** --- **(4)** If \( X \) is a geometric random variable \( \text{Geometric}(p) \), i.e., \( P(X=k) = p(1-p)^k, k=0,1,2,\ldots \), then \( E(X) \) is - [ ] \( \frac{1}{p} \) ◉ - [ ] 0 - [ ] \( p \) - [ ] \( (1/p)-1 \) - [ ] \( (1/p)+1 \) - [ ] N/A **(5)** If \( X \) is a normal \( N(0,1) \) random variable then \( E(X) \) is - [ ] 0 ◉ - [ ] 1 - [ ] -1 - [ ] \( +\infty \) - [ ] \(-\infty \) - [ ] N/A **(6)** Find the variance of \( X \) when \( X \sim \text{Geometric}(p) \). The correct answer is - [ ] \( \frac{1-p}{p^2} \) ◉ - [ ] \( \frac{1}{p^2} \) - [ ] \( \frac{1}{p} \) - [ ] \( \frac{1}{p} - 1 \) - [ ] None of the above - [ ] N/A --- Each question provides a multiple-choice format where the correct response is marked with a filled circle (◉).
Expert Solution
Step 1: geometric distribution( Question 4 and 6)

Probability homework question answer, step 1, image 1

Probability homework question answer, step 1, image 2

So. E(X) = 1/P

and Var(X) = (1-p)/(p^2)

steps

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