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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Question
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
---
Each question provides a multiple-choice format where the correct response is marked with a filled circle (◉).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F421db798-cca4-4efb-a6a9-3775d86708c7%2F40f6dbc0-98f5-40ee-abe8-eea868c9b255%2Ffl7zyx_processed.png&w=3840&q=75)
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
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1: geometric distribution( Question 4 and 6)
So. E(X) = 1/P
and Var(X) = (1-p)/(p^2)
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
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