Suppose a random variable has a continuous uniform distribution between 0 and 10, such that its probability density function is: f(x) = 1/10. a. What is the cumulative density function for x? b. What is the mean (expected value) of x? c. What is the variance of x? d. According to Chebychef's rule, what is the smallest probability a random x will within 2 standard deviations of its mean? i.e. P(x-μ<2*o) e. What is the exact probability that a random x will fall within 2 standard deviations of its mean for this uniform distribution?

Suppose a random variable has a continuous uniform distribution between 0 and 10, such that its probability density function is: f(x) = 1/10. a. What is the cumulative density function for x? b. What is the mean (expected value) of x? c. What is the variance of x? d. According to Chebychef's rule, what is the smallest probability a random x will within 2 standard deviations of its mean? i.e. P(x-μ<2*o) e. What is the exact probability that a random x will fall within 2 standard deviations of its mean for this uniform distribution?

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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Question

**Uniform Distribution Problem**

Suppose a random variable has a continuous uniform distribution between 0 and 10, such that its probability density function is: \( f(x) = 1/10 \).

**Questions:**

a. What is the cumulative density function for \( x \)?

b. What is the mean (expected value) of \( x \)?

c. What is the variance of \( x \)?

d. According to Chebychev's rule, what is the smallest probability a random \( x \) will be within 2 standard deviations of its mean?
- i.e. \( P(|x - \mu| < 2 \ast \sigma) \)

e. What is the exact probability that a random \( x \) will fall within 2 standard deviations of its mean for this uniform distribution?

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d. According to Chebychev’s rule, what is the smallest probability a random x will within 2 standard deviations of its mean?
i.e. \( P(|x - \mu| < 2 \ast \sigma) \)

e. What is the exact probability that a random x will fall within 2 standard deviations of its mean for this uniform distribution?

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