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Suppose a college professor never finishes her lecture before the end of the class period, and always finishes within five minutes after the class period is supposed to end. Let X = time that elapses between the end of the class period and the actual end of the lecture. Suppose the pdf of X is f(x) = kx³/2 0≤x≤ 5 and 0 otherwise. Find the value of k that makes f(x) a legitimate probability density function and use that value of k to find the probability that the lecture ends less than 3 minutes after the class period is supposed to end.

Suppose a college professor never finishes her lecture before the end of the class period, and always finishes within five minutes after the class period is supposed to end. Let X = time that elapses between the end of the class period and the actual end of the lecture. Suppose the pdf of X is f(x) = kx³/2 0≤x≤ 5 and 0 otherwise. Find the value of k that makes f(x) a legitimate probability density function and use that value of k to find the probability that the lecture ends less than 3 minutes after the class period is supposed to end.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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MX Suppose a college professor never finishes her lecture before the end of the class period, and always finishes within five minutes after the class period is supposed to end. Let X = time that elapses between the end of the class period and the actual end of the lecture. Suppose the pdf of X is f(x) = kx³/2 0 ≤ x ≤ 5 and 0 otherwise. Find the value of k that makes f(x) a legitimate probability density function and use that value of k to find the probability that the lecture ends less than 3 minutes after the class period is supposed to end. Please write complete
Transcribed Image Text:MX Suppose a college professor never finishes her lecture before the end of the class period, and always finishes within five minutes after the class period is supposed to end. Let X = time that elapses between the end of the class period and the actual end of the lecture. Suppose the pdf of X is f(x) = kx³/2 0 ≤ x ≤ 5 and 0 otherwise. Find the value of k that makes f(x) a legitimate probability density function and use that value of k to find the probability that the lecture ends less than 3 minutes after the class period is supposed to end. Please write complete
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