4 9. Let p(x) for x > 0 (and p(x) = 0 if x < 0). T(1+(2x)²) (a) Show that p is a probability density function. (b) If X is the associated random variable, find the median of X. (c) Show that the mean of X is infinite. This is strange: A finite amount of "mass" can be distributed along the positive number line in a way that the line does not balance at any point, but instead tips infinitely hard to the right at each location.

4 9. Let p(x) for x > 0 (and p(x) = 0 if x < 0). T(1+(2x)²) (a) Show that p is a probability density function. (b) If X is the associated random variable, find the median of X. (c) Show that the mean of X is infinite. This is strange: A finite amount of "mass" can be distributed along the positive number line in a way that the line does not balance at any point, but instead tips infinitely hard to the right at each location.

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...

See similar textbooks

Similar questions

do al otherwise not
Consider the probability density fx (x) = a. eb x! where X is random variable whose allowable values range from x = -o to + o. Find (a) the CDF (b) the relation between a and b (c) the probability that x lies between 1 and 2.
The probability that none of the three bulbs in a set of traffic lights will have to be replaced during the first 1200 hours of operation if the lifetime X of a bulb (in thousands of hours) is a random variable with probability density function f(x) = 6[0.25-(x-1.5)2] when 1 ≤ x ≤ 2 and f(x) = 0 otherwise is
The service life T (this year) of a particular type of electric toothbrush is assumed to have the probability density f given by: see figure question (a) Find the probability that a randomly selected toothbrush (of this type) has a lifespan of more than 2 years.(b) Assume that a toothbrush of the same type has been working for one year already. What is the probability that it works for at least another 3 years?(c) What is the probability that the average lifespan of T¯ for 90 independent toothbrushes is greater than 2.1 years?
Suppose that X and Y are statistically independent and identically distributed uniform random variables on (0,1). (a) Write down the joint probability density function fx,y(x,y) of X and Y on its support.
3. Let X and Y be two independent random variables with identical probability density function given by e- for x > 0 f(x) = elsewhere. What is the probability density function of W= max{X, Y } ?
1. Let X be a random number from (0, 1). Find the probability density function of Y = 1/X.