2. Let \( X \) be a random variable with the following density.\[f(x) = \begin{cases} c(1-x)^3 & \text{if } x \in (0,1), \\0 & \text{otherwise}.\end{cases}\]- (i) Find the constant \( c \) and then \( E(X) \) when \( X \) has the above density.- (ii) Find \( E(X^2) \) when \( X \) has the above density.- (iii) Find \( Std(X) \) when \( X \) has the above density.

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Answered: 2. Let X be a random variable with the…

A First Course in Probability (10th Edition)

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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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2. Let X be a random variable with the following density. { c(1– x)3 if r € (0, 1), otherwise. f(x) (i) Find the constant c and then E(X) when X has the above density. (ii) Find E(X²) when X has the above density. (iii) Find Std(X) when X has the above density.