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(8) Find the variance of X when X is distributed as N(0, 1). The correct answer is 2 N/A (Select One) (9) Find Std(X) when X is a continuous random variable with the following given density. (i) f(z) = 2(1 – z), on [0, 1], (iii) f(z) = 0.01e 0.01z on (0, 00), (v) f(z) = 3/z', on (1, 00), (vii) f(z) = 2ze², on [0, 00), (ix) f(x) = sin z, on (0, x), 1/18 (18)–1/2 1 18 None of the above N/A (i- Select One)

(8) Find the variance of X when X is distributed as N(0, 1). The correct answer is 2 N/A (Select One) (9) Find Std(X) when X is a continuous random variable with the following given density. (i) f(z) = 2(1 – z), on [0, 1], (iii) f(z) = 0.01e 0.01z on (0, 00), (v) f(z) = 3/z', on (1, 00), (vii) f(z) = 2ze², on [0, 00), (ix) f(x) = sin z, on (0, x), 1/18 (18)–1/2 1 18 None of the above N/A (i- Select One)

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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**Exercise Problems and Solutions** --- **Problem 7** Find the variance of \( X \) when \( X \) is \( \text{Exp}(\lambda) \). - Choices: - \(\frac{1}{\lambda}\) - \(\frac{2}{\lambda}\) - \(\frac{2}{\lambda^2}\) - \(\frac{1}{\lambda^2}\) - None of the above - Correct answer: N/A --- **Problem 8** Find the variance of \( X \) when \( X \) is distributed as \( N(0, 1) \). - Choices: - 0 - -1 - 1 - 2 - -2 - Correct answer: N/A --- **Problem 9** Find \(\text{Std}(X)\) when \( X \) is a continuous random variable with the following given density: - Definitions: 1. \( f(x) = 2(1-x) \), on \([0,1]\), 2. \( f(x) = 0.01e^{-0.01x} \), on \([0, \infty)\), 3. \( f(x) = 3/x^4 \), on \([1, \infty)\), 4. \( f(x) = 2xe^{-x^2} \), on \([0,\infty)\), 5. \( f(x) = \frac{1}{2} \sin x \), on \((0, \pi)\). - Choices: - 1 - \(\frac{1}{18}\) - 18 - \( (18)^{-1/2} \) - None of the above - Correct answer: N/A --- **Graph or Diagram Explanation:** There are no graphs or diagrams in the image. The document is a series of multiple choice questions (MCQs) designed to test knowledge on statistical distributions, specifically focusing on variance and standard deviation calculations.
Transcribed Image Text:**Exercise Problems and Solutions** --- **Problem 7** Find the variance of \( X \) when \( X \) is \( \text{Exp}(\lambda) \). - Choices: - \(\frac{1}{\lambda}\) - \(\frac{2}{\lambda}\) - \(\frac{2}{\lambda^2}\) - \(\frac{1}{\lambda^2}\) - None of the above - Correct answer: N/A --- **Problem 8** Find the variance of \( X \) when \( X \) is distributed as \( N(0, 1) \). - Choices: - 0 - -1 - 1 - 2 - -2 - Correct answer: N/A --- **Problem 9** Find \(\text{Std}(X)\) when \( X \) is a continuous random variable with the following given density: - Definitions: 1. \( f(x) = 2(1-x) \), on \([0,1]\), 2. \( f(x) = 0.01e^{-0.01x} \), on \([0, \infty)\), 3. \( f(x) = 3/x^4 \), on \([1, \infty)\), 4. \( f(x) = 2xe^{-x^2} \), on \([0,\infty)\), 5. \( f(x) = \frac{1}{2} \sin x \), on \((0, \pi)\). - Choices: - 1 - \(\frac{1}{18}\) - 18 - \( (18)^{-1/2} \) - None of the above - Correct answer: N/A --- **Graph or Diagram Explanation:** There are no graphs or diagrams in the image. The document is a series of multiple choice questions (MCQs) designed to test knowledge on statistical distributions, specifically focusing on variance and standard deviation calculations.
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