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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.

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.

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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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.
Transcribed Image Text: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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