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devote on overtime. The cumulative distribution function of T is given by 0, t <0 > = {m (2²³²- 1²). F(t) = m(2t³-t¹), 0≤t≤1.5 1, t> 1.5. a) Justify the value of m so that it satisfies the cumulative distribution function. [CO2, A3] 1 b) Find the proportion of employees who devote more than 1 hour on overtime. [CO3, C2] c) Find the probability density function f(t) of T. [CO3, C2] L

devote on overtime. The cumulative distribution function of T is given by 0, t <0 > = {m (2²³²- 1²). F(t) = m(2t³-t¹), 0≤t≤1.5 1, t> 1.5. a) Justify the value of m so that it satisfies the cumulative distribution function. [CO2, A3] 1 b) Find the proportion of employees who devote more than 1 hour on overtime. [CO3, C2] c) Find the probability density function f(t) of T. [CO3, C2] L

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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1. The continuous random variable T denotes the time in hours that employees devote on overtime. The cumulative distribution function of T is given by 0, = { m (20² - 12) F(t) = t < 0 -t¹), 0≤t≤ 1.5 t> 1.5. a) Justify the value of m so that it satisfies the cumulative distribution function. [CO2, A3] d) Find E(T). [CO3, C2] b) Find the proportion of employees who devote more than 1 hour on overtime. [CO3, C2] c) Find the probability density function f(t) of T. [CO3, C2] [ L e) An employee is chosen at random. Calculate the probability that the employee devoted more than 1 hour on overtime, given that the employed devoted more than the mean amount of time on overtime. [CO3, C3]
Transcribed Image Text:1. The continuous random variable T denotes the time in hours that employees devote on overtime. The cumulative distribution function of T is given by 0, = { m (20² - 12) F(t) = t < 0 -t¹), 0≤t≤ 1.5 t> 1.5. a) Justify the value of m so that it satisfies the cumulative distribution function. [CO2, A3] d) Find E(T). [CO3, C2] b) Find the proportion of employees who devote more than 1 hour on overtime. [CO3, C2] c) Find the probability density function f(t) of T. [CO3, C2] [ L e) An employee is chosen at random. Calculate the probability that the employee devoted more than 1 hour on overtime, given that the employed devoted more than the mean amount of time on overtime. [CO3, C3]
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