The lifespan X (years) of a species of pig has pdf f (x) = 3x2e−x^3 , 0 < x < ∞. What is the probability that a pig will live at least 1 year? Given that it lives 1 year, what is the conditional probability that it will live for at least another year?
The lifespan X (years) of a species of pig has pdf f (x) = 3x2e−x^3 , 0 < x < ∞. What is the probability that a pig will live at least 1 year? Given that it lives 1 year, what is the conditional probability that it will live for at least another year?
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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Question
The lifespan X (years) of a species of pig has pdf
f (x) = 3x2e−x^3 , 0 < x < ∞.
What is theprobability that a pig will live at least 1 year? Given that it lives 1 year, what is the conditional
probability that it will live for at least another year?
f (x) = 3x2e−x^3 , 0 < x < ∞.
What is the
probability that it will live for at least another year?
Expert Solution
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Step 1: Step by step solution for part a>
To find the probability that a pig will live at least 1 year, you need to calculate the integral of the probability density function (pdf) from 1 to infinity. The probability that a pig will live at least 1 year is given by:
To solve this integral, you can make a substitution. Let , which implies . The integral becomes:
Now, evaluate this integral from 1 to infinity:
So, the probability that a pig will live at least 1 year is .
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