Show that f (x, y) = 1/x, 0 < y < x < 1, is a joint

Question:

Show that f (x, y) = 1/x, 0 < y < x < 1, is a joint density function. Assuming that f is the joint density function of X,Y, find
(a) The marginal density of Y;
(b) The marginal density of X;
(c) E[X];
(d) E[Y].

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

A First Course In Probability

ISBN: 9789332519077

9th Edition

Authors: Sheldon Ross

See More Books

Question Posted: Oct 22, 2015 02:56 AM

See More Questions

Let f (x, y) = 24xy0 x 1, 0 y 1, 0 x + y 1 and let it equal 0 otherwise. (a) Show that f (x, y) is a joint probability density function. (b) Find E[X]. (c) Find E[Y].
1. Given that f (x) = ex + e-x/2 and g (x) = ex - e-x/2 show that [f (x)]2 - [g (x)]2 = 1. 2. Use a graphing utility to compare the graph of the function y = ex with the graph of each function.[n!...
Graph and discuss the continuity of the function (a) Show that f (x, y) 0 as (x, y) (0, 0) along any path through (0, 0) of the form y = mx a with 0 < a < 4. (b) Despite part (a), show that f is...
Since graduation from college, your friend William has become a highly paid and successful financial advisor. His list of clients is long, and his advice is sought by many. Discuss the merits of the...
Identify the maximum value, minimum value, median, first quartile, third quartile, and interquartile range. 50 55 60 65 7075 80 85 90 95 100 Ma
to include transfer times between part arrival and the f rst workstation, between workstations (both going forward and for reprocessing), and between the last workstation and the system exit. Assume...
The 10 critical success factors have been applied in a variety of settings and project types. Consider a project with which you have been involved. Did any of these factors emerge clearly as being...
Lamp Light Limited (LLL) in E9-11 calculates a fixed overhead rate based on budgeted fixed overhead of $32,400 and budgeted production of 24,000 units. Actual results were as follows: Number of units...
Total Cost of Capital Asset Purchase Brown Company purchased a piece of equipment for the price of $50,000. Prior to installing the equipment, they had to replace the flooring in the manufacturing...
Read the case study "Pharmacy Service Improvement at CVS (A and B) by Andrew McAfee, Harvard Business School, HBSP," and answer all the questions. 1. Model the original order fulfillment process at...
Two points are selected randomly on a line of length L so as to be on opposite sides of the midpoint of the line. [In other words, the two points X and Y are independent random variables such that X...
Suppose that 3 balls are chosen without replacement from an urn consisting of 5 white and 8 red balls. Let Xi equal 1 if the ith ball selected is white, and let it equal 0 otherwise. Give the joint...
Express the area of the following shaded regions in terms of (a) One or more integrals with respect to x. (b) One or more integrals with respect to y. You do not need to evaluate the integrals. -3 ...
Consider the following C functions and assembly code: int fun4 (int *ap, int *bp) ( int a = *ap; int bbp; return a+b; }) pushl ebp movl esp, ebp int fun5 (int *ap, int *bp) { int bbp; *bp + *ap;...
The position of a particle moving along the x-axis is given by x(t) = = 4.2 2.5t m. (Assume t is in seconds.) (a) At what time (in s) does the particle cross the origin? 1.68 S (b) What is the...
2. Boxes A and B are being pulled to the right by a rope attached to box B. Box A sits on top of box B, and both boxes accelerate together to the right at a rate of 1.75 m/s. The masses and...
You bought a 15-kilogram sack of unshelled peanuts for your restaurant. You weigh the sack three times on a balance, with the following results: Trial Mass (kg) 1 15.02 2 15.49 3 15.91 The results...
Two hikers leave the same tent at a campground and go separate ways. One hiker walks 8 miles directly south to Ashville, and the other hiker walks 14 miles directly northwest (i.e., N45W) to...
What is emotional design? How does this idea translate into user goals?
A container holds 2.0 mol of gas. The total average kinetic energy of the gas molecules in the container is equal to the kinetic energy of an 8.0 10-3-kg bullet with a speed of 770 m/s. What is the...
Why should accounting students learn about business process management
The number of accidents in a production facility has a Poisson distribution with a mean of 2.6 per month. a. For a given month what is the probability there will be fewer than 2 accidents? b. For a...
A customer service center in India receives, on average, 4.2 telephone calls per minute. If the distribution of calls is Poisson, what is the probability of receiving at least 3 calls during a...
Records indicate that, on average, 3.2 breakdowns per day occur on an urban highway during the morning rush hour. Assume that the distribution is Poisson. a. Find the probability that on any given...
Explain the following: Understand the PPE acquisition (or investing) cycle and related significant transactions and source documents Understand the relevant assertions/objectives about PPE balances...
Problem 3 Progress Company acquired 6 0 % of Stall Corporation on 1 2 0 2 0 . Fair values of Stall's assets and liabilities approximated book values on that date. Progress uses the initial value...
C: The sor at the poopecin 0ieund to twe oxind places)

Show that f (x, y) = 1/x, 0 < y < x < 1, is a joint

Question:

Step by Step Answer:

a b c 12 d Integr...View the full answer

A First Course In Probability

Students also viewed these Statistics questions