Question: Show that a uniformly distributed random variable X with probability density function has expected value 1 f(x) = b - a 0 if a x

Show that a uniformly distributed random variable X with probability density function


1 f(x) = b - a 0 if a x b otherwise


has expected value


image

1 f(x) = b - a 0 if a x b otherwise

Step by Step Solution

★★★★★

3.36 Rating (159 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

fx EX 1 ba 0 b X ... 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 With Applications Questions!

Q:

Show that an exponentially distributed random variable X with probability density function has expected value E(X) = 1/k. f(x) = = [ke-kx lo if x 0 if x

Q:

What is the relationship between the amount spent per week on recreation and the size of the family? A sample of 10 families in the New York area provided the following data: Family Size...

Q:

Given two independent, wide-sense stationary random processes X(t) and Y(t) with auto correlation functions R x () and R Y (), respectively. (a) Show that the auto correlation function R Z () of...

Q:

The waiting time, X minutes for a customer in a certain queue is a uniformly distributed random variable with the probability density function given by U(0,10). (i) Find the cumulative distribution...

Q:

For the Exponentially Distributed random variable X with probability density function (pdf) as tollows: fx(x) = dea x>0 otherwise Homework 1: Show thue derivation of tlu: following: 1 v E(X) Hx - B...

Q:

5. It is known that the random variable X has probability density function of the form f( 210 ) = Be-210, 0

Q:

5. Consider the discrete random variable X whose probability density function is x +1 f ( x ) = 10 , x E {0,1,2,3} (10 points) (a) Graph the pdf. (b) Give the cumulative distribution function (cdf)...

Q:

5. Consider the discrete random variable X whose probability density function is x +1 f ( x ) = 10 , X E {0,1,2,3} (10 points) (a) Graph the pdf. (b) Give the cumulative distribution function (cdf)...

Q:

Course Name: Probability and Random Variables Course Code: 1 1 0 7 1 3 1 2 0 Instructor: Dr . Naser Hamad and Dr . Sanaa Salama Assignment Deadline: The assignment should be submitted by 2 1 s t of...

Q:

Assignment One [12 Marks] Consider a random variable X with probability density function f(x) and mean . (i) Define algebraically the following risk measures for X: (a) shortfall probability below a...

Q:

What is "preset" during installation of bridge bearings?

Q:

Min Industries had selected unadjusted balances as shown below at year-end. A search on the Internet showed fair values on December 31, 2014, of: CashCo, $18; Wells, $0.70. Prepare the appropriate...

Q:

8.9 Write a short note on average outgoing quality limit.

Q:

What visual features facilitate the detection of emotions in facial expressions?

Q:

Assess the statistical significance of the individual risk factors? Cardiovascular Disease Sudden death is an important, lethal cardiovascular endpoint. Most previous studies of risk factors for...

Q:

What do these statistical tests mean in this instance? Cardiovascular Disease Sudden death is an important, lethal cardiovascular endpoint. Most previous studies of risk factors for sudden death have...

Q:

Compute the OR relating the additional risk of sudden death per 100-centiliter (cL) decrease in vital capacity after adjustment for the other risk factors? Cardiovascular Disease Sudden death is an...

Q:

Which of the following events is an intercompany transaction? A) a capital contribution B) a parent corporation's sale of stock of a subsidiary corporation to a nonmember of the group C) dividend...

Q:

Please solve this question as soon as possible within an hour and a half with show all the steps and calculations (for thumbs up) AMG Naturopathic Clinic uses patient-visits as its measure of...

Q:

The following information is available about a signed agreement between two entities: The entities have agreed to specific performance obligations. The entities have agreed on a price related to the...