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?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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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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