C1. Let X be a continuous random variable with PDFf(x) = (2-x)²for -1 < x < cand f(x) = 0 otherwise.(a) Explaining your work, find the value of the constant c.(b) What is P(X > 1)?(c) Calculate the expectation of X.(d) Calculate the variance of X.

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Answered: C1. Let X be a continuous random…

A First Course in Probability (10th Edition)

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Author:Sheldon Ross

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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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C1. Let X be a continuous random variable with PDF f(x) = (2-x) for -1 ≤x≤c and f(x) = 0 otherwise. (a) Explaining your work, find the value of the constant c. (b) What is P(X > 1)? (c) Calculate the expectation ofX. (d) Calculate the variance of X.