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...
icon
Related questions
Question
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?
 
Expert Solution
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 .

steps

Step by step

Solved in 3 steps with 4 images

Blurred answer
Similar questions
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON