Let's say p a real function p by:1P(x) = 5ex ERa. Why is the function p a probability density?b. In the sequence, X is a random variable with probability density p.Calculate P(X 2 0) ?c. Calculate the expected value of Xd. Calculate the variance of X

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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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Let X be a random variable that follows the beta distribution. This random variable is continuous and is defined over the interval from 0 to 1. The probability density function is given by whereand are integers, whose values determine the shape of the probability density function. Because X varies between 0 and 1, we can think of X as the probability that some event (say) E occurs or the proportion of times an event occurs in some population. For example, E could denote the event that a critical part in a newly designed car will lead to a catastrophic failure in accidents at high speeds. The expected value (i.e., mean) of this random variable is []. That is, . The Excel commands for the beta random variable are =beta.dist(x,,,true,0,1) for the cumulative probability distribution, and =beta.dist(x,,,false,0,1) for the probability density function. (a) Now, think in Bayesian terms.…

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Let's say p a real function p by: 1 P(x) =e-*, x E R a. Why is the function p a probability density? b. In the sequence, X is a random variable with probability density p. Calculate P(X > 0) ? c. Calculate the expected value of X