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a. Verify that the function given is a valid probability density function. b. Determine the cumulative density function (cdf) of the random variable X. c. Compute the probability that X is less than or equal to 0.5.

a. Verify that the function given is a valid probability density function. b. Determine the cumulative density function (cdf) of the random variable X. c. Compute the probability that X is less than or equal to 0.5.

MATLAB: An Introduction with Applications
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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Please answer the whole question quickly and correctly The probability density function (pdf) of a continuous random variable X is given as follows: a. Verify that the function given is a valid probability density function. b. Determine the cumulative density function (cdf) of the random variable X. c. Compute the probability that X is less than or equal to 0.5. d. Compute the probability that X is greater than or equal to 1.5. e. Compute the probability that X is between 0.5 and 1.5. f. Compute the probability that X is exactly 0.5. g. Compute the expected value of the random variable X. h. Compute the variance of the random variable X. i. Find E[3X+4]. j. Find E[X2]. k. Find Var[-3X].
Transcribed Image Text:Please answer the whole question quickly and correctly The probability density function (pdf) of a continuous random variable X is given as follows: a. Verify that the function given is a valid probability density function. b. Determine the cumulative density function (cdf) of the random variable X. c. Compute the probability that X is less than or equal to 0.5. d. Compute the probability that X is greater than or equal to 1.5. e. Compute the probability that X is between 0.5 and 1.5. f. Compute the probability that X is exactly 0.5. g. Compute the expected value of the random variable X. h. Compute the variance of the random variable X. i. Find E[3X+4]. j. Find E[X2]. k. Find Var[-3X].
f(x) = 11--² 0 x<0 0<x< 1 2 1<x<2 x ≥ 2
Transcribed Image Text:f(x) = 11--² 0 x<0 0<x< 1 2 1<x<2 x ≥ 2
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