Chapters: Expected value & Variance of a continuous random variable **Q1. Calculate $ E(Y) $ for the following PDFs:** a. $ f(y) = 3(1-y)^2, \quad 0 \leq y \leq 1 $ b. $ f(y) = 4ye^{-2y}, \quad y \geq 0 $ ---**Q2.** If $ Y $ has PDF $ f(y) = 2y $ for $ 0 < y < 1 $, then $ E(Y) = \frac{2}{3} $. Define the random variable $ W $ to be the squared deviation of $ Y $ from its mean, that is, $ W = \left(Y - \frac{2}{3}\right)^2 $. Find $ E(W) $.

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Q1. Calculate E(Y) for the following pdfs: a. f(y) = 3(1 – y)², 0 < y < 1 b. f(y) = 4ye-2", y > 0

A First Course in Probability (10th Edition)

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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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Question

Chapters: Expected value & Variance of a continuous random variable

**Q1. Calculate $ E(Y) $ for the following PDFs:**

a. $ f(y) = 3(1-y)^2, \quad 0 \leq y \leq 1 $

b. $ f(y) = 4ye^{-2y}, \quad y \geq 0 $

---

**Q2.** If $ Y $ has PDF $ f(y) = 2y $ for $ 0 < y < 1 $, then $ E(Y) = \frac{2}{3} $. Define the random variable $ W $ to be the squared deviation of $ Y $ from its mean, that is, $ W = \left(Y - \frac{2}{3}\right)^2 $. Find $ E(W) $.

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