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4. The pdf of X is f(x) = 24 (27 - x³) for 0 < x < 3, and 0 otherwise. a) Find P(1 < X < 2). b) Find E(X). c) Find the third moment of X.

4. The pdf of X is f(x) = 24 (27 - x³) for 0 < x < 3, and 0 otherwise. a) Find P(1 < X < 2). b) Find E(X). c) Find the third moment of X.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 52E
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4. The pdf of X is f(x) = 243 (27 − x³) for 0 < x < 3, and 0 otherwise. a) Find P(1 < X < 2). b) Find E(X). c) Find the third moment of X. d) Find E[X(2X² - 3) + 10].
Transcribed Image Text:4. The pdf of X is f(x) = 243 (27 − x³) for 0 < x < 3, and 0 otherwise. a) Find P(1 < X < 2). b) Find E(X). c) Find the third moment of X. d) Find E[X(2X² - 3) + 10].
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