Let X be the time in hours that the battery of a solar calculator functions properly between exposures to light sufficient to recharge it. Suppose the density of X is given by: f(x) = (50/6)x^-3                              2 < x < 10. a) Verify that this is a valid continuous density. b) Calculate the expression for the cumulative distribution function of X and use it to calculate the probability that the charge of a randomly selected solar cell will last at most four hours before it needs to be used. at most four hours before it needs to be recharged. c) Calculate the average time that a battery charge lasts before it needs to be recharged. d) Calculate E[X2] and use its value to determine the variance of X.

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
icon
Concept explainers
Question

Let X be the time in hours that the battery of a solar calculator functions properly between exposures to light sufficient to recharge it. Suppose the density of X is given by:
f(x) = (50/6)x^-3                              2 < x < 10.
a) Verify that this is a valid continuous density.


b) Calculate the expression for the cumulative distribution function of X and use it to calculate the probability that the charge of a randomly selected solar cell will last at most four hours before it needs to be used.
at most four hours before it needs to be recharged.


c) Calculate the average time that a battery charge lasts before it needs to be recharged.


d) Calculate E[X2] and use its value to determine the variance of X.

 

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 images

Blurred answer
Knowledge Booster
Continuous Probability Distribution
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.
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