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Let X ~ Exponmential(2) and Y = 2 + 3X. %3D a. Find P(X > 2). b. Find EY and Var(Y). c. Find P(X > 2|Y < 11).

Let X ~ Exponmential(2) and Y = 2 + 3X. %3D a. Find P(X > 2). b. Find EY and Var(Y). c. Find P(X > 2|Y < 11).

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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Question
**Problem 11** Let \( X \sim \text{Exponential}(2) \) and \( Y = 2 + 3X \). a. Find \( P(X > 2) \). b. Find \( E(Y) \) and \( \text{Var}(Y) \). c. Find \( P(X > 2 \mid Y < 11) \).
Transcribed Image Text:**Problem 11** Let \( X \sim \text{Exponential}(2) \) and \( Y = 2 + 3X \). a. Find \( P(X > 2) \). b. Find \( E(Y) \) and \( \text{Var}(Y) \). c. Find \( P(X > 2 \mid Y < 11) \).
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