**Uniform Random Variable Analysis**A uniform random variable \( X \) has a probability density given by:\[ f(x) = \begin{cases} \frac{1}{2} & \text{for } 0 \leq x \leq 2 \\ 0 & \text{otherwise} \end{cases} \]The **mean** of \( X \) is 1, and the **variance** is \( 1/3 \).**Tasks**(a) Find the probability that \( X \) takes values within 2 standard deviations of the mean, i.e., \( P(|X - 1| < 2\sigma) \).(b) Find a bound for the probability in part (a) using the Chebychev's inequality.

Answered: A uniform random variable X has a…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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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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A random variable X follows a uniform continuous distribution on the range [0, B]. Use mathematical expectation to show the mean is B/2
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X is the number of successes in 10 independent Bernoulli trials. The variance of X is equal to 3/4 of the expectation of X (ie Var(X)=0.75E(X)). The probability that X is less than 2 is equal to_____. Please fill in the blank.
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