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1. The probability density function (pdf) of a continuous random variable X is given as follows: x< 0 4 0sx<1 S(x)= 2 Isx<2 x2 2 Determine the cumulative density function (cdf) of the a. random variable X b. Compute the probability that X is less than or equal to 0.5 c. Compute the probability that X is greater than or equal to 1.5

1. The probability density function (pdf) of a continuous random variable X is given as follows: x< 0 4 0sx<1 S(x)= 2 Isx<2 x2 2 Determine the cumulative density function (cdf) of the a. random variable X b. Compute the probability that X is less than or equal to 0.5 c. Compute the probability that X is greater than or equal to 1.5

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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1. The probability density function (pdf) of a continuous random variable \( X \) is given as follows: \[ f(x) = \begin{cases} 0 & x < 0 \\ \frac{9}{4}x^2 & 0 \leq x < 1 \\ 1 - \frac{x}{2} & 1 \leq x < 2 \\ 0 & x \geq 2 \end{cases} \] a. Determine the cumulative density function (cdf) of the random variable \( X \). b. Compute the probability that \( X \) is less than or equal to 0.5. c. Compute the probability that \( X \) is greater than or equal to 1.5. d. Compute the probability that \( X \) is between 0.5 and 1.5.
Transcribed Image Text:1. The probability density function (pdf) of a continuous random variable \( X \) is given as follows: \[ f(x) = \begin{cases} 0 & x < 0 \\ \frac{9}{4}x^2 & 0 \leq x < 1 \\ 1 - \frac{x}{2} & 1 \leq x < 2 \\ 0 & x \geq 2 \end{cases} \] a. Determine the cumulative density function (cdf) of the random variable \( X \). b. Compute the probability that \( X \) is less than or equal to 0.5. c. Compute the probability that \( X \) is greater than or equal to 1.5. d. Compute the probability that \( X \) is between 0.5 and 1.5.
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