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Let f(x) = k(3x - x²) if 0 ≤ x ≤ 3 and f(x) = 0 if x <0 or x > 3. a) For what value of k is f a probability density function? b) For that value of k, find P(X > 1).

Let f(x) = k(3x - x²) if 0 ≤ x ≤ 3 and f(x) = 0 if x <0 or x > 3. a) For what value of k is f a probability density function? b) For that value of k, find P(X > 1).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Let f(x) = k(3x - x²) if 0 ≤ x ≤ 3 and f(x) = 0 if x <0 or x > 3. a) For what value of k is f a probability density function? b) For that value of k, find P(X > 1).
Transcribed Image Text:Let f(x) = k(3x - x²) if 0 ≤ x ≤ 3 and f(x) = 0 if x <0 or x > 3. a) For what value of k is f a probability density function? b) For that value of k, find P(X > 1).
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