Question: Show that the density function p(x) = 2/(x 2 + 1) on [0,) has infinite mean.

Show that the density function p(x) = 2/π(x2 + 1) on [0,∞) has infinite mean.

Step by Step Solution

★★★★★

3.50 Rating (153 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

To verify that p is a probability density function note that R ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Calculus 4th Questions!

Q:

Recall that the density function of a normal distribution with mean u and standard deviation o > 0 is 1 -(-)2/(202) 2 e This is an extremely important family of functions in statistics, and models...

Q:

The random variable X has probability density function as follows: a. Graph the probability density function for X. b. Show that the density has the properties of a proper probability density...

Q:

Suppose that the density function p(xl) is defined as follows for x = 1, 2, 3, ... and = 1, 2, 3, .... If is even, then Show that, for any x the data intuitively give equal support to the three...

Q:

The percentage of an additive in a certain type of food has the following density function kx 3 (1 x) if 0 x 1 f(x) = 0 otherwise. (a) Find k (b) Find the distribution function for the random...

Q:

Which answer do I choose? Let X be an exponential random variable with probability density function p x (2:) = e"? for .1: 2 0. Which of the answers below is the correct combination of P(2X S 2) and...

Q:

2. Let X be a random variable with probability density function f (x) = 1/4 if x (1, 3) 0 otherwise. (a) Find MX(t), E(X), and Var(X). (b) Using MX(t), calculate E(X). Hint: Note that by the...

Q:

10-32. Let {X1,X2, . . . ,Xn} be a set of sample random variables drawn from the probability density function f (x; ) = (1 )x1, x = 1, 2, . . . ; 0

Q:

A couple of nights per week you babysit a 7-year-old boy. He is obsessed with TV but he can only get 30 minutes of screen time. After that, you start to ask him to turn the TV off but of course, he...

Q:

This exercise will lead you through a proof of Chebyshevs inequality. Let X be a continuous random variable with probability density function f (x). Suppose that P(X

Q:

A random variable X has the density function f(x) = (x + x) if x [0, 1] 0 otherwise a) Determine the value of c. b) Compute E( 1 X ). c) Determine the probability density function of Y = X2 . A...

Q:

Audible Sound provided the amplitude is sufficiently great, the human ear can respond to longitudinal waves over a range of frequencies from about 20.0 Hz to about 20.0 kHz. (a) If you were to mark...

Q:

Suppose a corporate bond that reaches maturity on 09/01/2040 is trading today (9/29/2020) for $803. The bond certificate indicates that the stated coupon rate for this bond is 6% and that the coupon...

Q:

A stocks total risk is measured by: 1 . Beta 2 . Multiplying standard deviation by beta 3 standard deviation

Q:

In Problem 10.132, suppose a fleet of 50 ships is to be handled at the docks and each ship spends an average of 20 days at sea. Determine the optimum number of unloading spaces.

Q:

True or False If x = 3 is a vertical asymptote of a rational function R, then lim x3 |R(x)| = .

Q:

Use transformations to graph y = 2x.

Q:

Convert angle in degrees to radians. Express your answer as a multiple of . 210

Q:

Gloria Martinez, an NRA, is a professional golfer. She played in seven tournaments in the United States in the current year and earned $250,000 in prizes from these tournaments. She deposited the...

Q:

1. Given two integer numbers return their product only if the product is equal to or less than 500 , else return their sum

Q:

You are considering buying a condo in NYC. You are borrowing $500,000. You have two financing options: Option A: 30-year mortgage 7.8% APR and 1 point Option B: 30-year mortgage 7.2% APR with two...