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The median of a continuous random variable with pdf f(x) is a real number m such that: ·m *** f(x)dx 91 [ f(x)dx Similarly, the first and third quartiles of a continuous random variable with pdf f(x) are real numbers 91, 93 such that - = 1 1 2 93 [ f(x) dx = 314 1+ax Let f(x) = ¹+ for −1≤ x ≤ 1 and f(x) = 0 otherwise, where -1 ≤ a ≤ 1. Show that f is a density, and find the corresponding cdf. Find the quartiles and the median of the distribution in terms of a.

The median of a continuous random variable with pdf f(x) is a real number m such that: ·m *** f(x)dx 91 [ f(x)dx Similarly, the first and third quartiles of a continuous random variable with pdf f(x) are real numbers 91, 93 such that - = 1 1 2 93 [ f(x) dx = 314 1+ax Let f(x) = ¹+ for −1≤ x ≤ 1 and f(x) = 0 otherwise, where -1 ≤ a ≤ 1. Show that f is a density, and find the corresponding cdf. Find the quartiles and the median of the distribution in terms of a.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 3CR
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The median of a continuous random variable with pdf f(x) is a real number m such that: [ f(x)dx = 1/2 Similarly, the first and third quartiles of a continuous random variable with pdf f(x) are real numbers 91,93 such that 91 93 1 3 [ f(x)dx = ² [ f(x) dx = ³ 4 Let f(x) = ¹+ for −1 ≤ x ≤ 1 and f(x) = 0 otherwise, where −1 ≤ a ≤ 1. Show that f is a density, and find the corresponding cdf. Find the quartiles and the median of the distribution in terms of a.
Transcribed Image Text:The median of a continuous random variable with pdf f(x) is a real number m such that: [ f(x)dx = 1/2 Similarly, the first and third quartiles of a continuous random variable with pdf f(x) are real numbers 91,93 such that 91 93 1 3 [ f(x)dx = ² [ f(x) dx = ³ 4 Let f(x) = ¹+ for −1 ≤ x ≤ 1 and f(x) = 0 otherwise, where −1 ≤ a ≤ 1. Show that f is a density, and find the corresponding cdf. Find the quartiles and the median of the distribution in terms of a.
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