7. A piece of equipment has a lifetime T (measured in years) that is a continuous ran- dom variable with cumulative distribution function F(t) = 1 – e/10 – (1/10) e¯/10 for all t> 0. a. What is the probability density function of T? b. What is the probability that a piece of equipment survives more than 20 years? c. What is the probability that a piece of equipment survives more than 10 years but fewer than 20 years? d. What is the probability that a piece of equipment survives more than 20 years given that it has survived for 10 years?
7. A piece of equipment has a lifetime T (measured in years) that is a continuous ran- dom variable with cumulative distribution function F(t) = 1 – e/10 – (1/10) e¯/10 for all t> 0. a. What is the probability density function of T? b. What is the probability that a piece of equipment survives more than 20 years? c. What is the probability that a piece of equipment survives more than 10 years but fewer than 20 years? d. What is the probability that a piece of equipment survives more than 20 years given that it has survived for 10 years?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text:7. A piece of equipment has a lifetime T (measured in years) that is a continuous ran-
dom variable with cumulative distribution function
F(t) = 1 – e/10 – (1/10) e¯/10
for all t> 0.
a. What is the probability density function of T?
b. What is the probability that a piece of equipment survives more than 20 years?
c. What is the probability that a piece of equipment survives more than 10 years
but fewer than 20 years?
d. What is the probability that a piece of equipment survives more than 20 years
given that it has survived for 10 years?
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