Consider the joint probability density function shown below:fx.y(x, y) = 2/33X21y=a) Find Fx,y(x, y).b) Find the marginal fy(y).c) Find E[X|Y = y].(Note that the equation for the line isy = 3x and fx,y(x, y) is 2/3 for0≤3x≤y≤3)Fxy (x) = f (x). fy (y)2

Step 1:To find the joint cumulative distribution function (CDF) FX,Y(x,y) we integrate the joint…

Answered: Consider the joint probability density…

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

The cumulative distribution function of the continuous uniform distribution between con- stants a and b is given by F(x) = P(X ≤ x) = x-a - a x b (a) The probability density function is f(x) = F(r). Find the form of f(x). (b) Find the derivative of f(x) for x = [a, b]. Is f(x) decreasing, increasing or flat in this region? (c) Does f(x) have a single maximum in the region [a,b]? If so, what is it, or if not, why not?
For the joint probability density function f(x.y)= k(x² +y²), -2
Consider the joint pdf fxy(x, y) = cxy, for 0
C, D, and E
Consider the Prelec function w(p) = e−1.5(− ln p) . Consider only interior fixed points (so ignore the fixed points w(0) = 0 and w(1) = 1). Let p be the probability corresponding to the point of inflexion and p∗ the fixed point. Which of the following statements is true? (A) p < p∗. (B) p > p∗. (C) p = p∗. (D) There is insufficient information to determine the relative sizes of p, p∗.
The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 31 hours and the median is 27.2hours. Twenty-four of the families in the sample turned on the television for 16 hours or less for the week. The 8th percentile of the data is 16 hours. Based on the given information, determine if the following statement is true or false. The first quartile is less than 16 hours.
5. Determine the value of c that makes the function f (x, y) = c(x + y) a joint probability density function over the range 0 < x < 3 and 0 < y < x. Answer is C = 2/27 a. From the answer in Question 5, Determine the marginal probability distribution of X. b. From the answer in Question 5, Determine the conditional probability distribution of X given that Y = 2. c. From the answer in Question 5, Determine E(Y | X = 1). (up to 6 decimal place)

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS

Consider the joint probability density function shown below: fx.y(x, y) = 2/3 3 X 21 y= a) Find Fx,y(x, y). b) Find the marginal fy(y). c) Find E[X|Y = y]. (Note that the equation for the line is y = 3x and fx,y(x, y) is 2/3 for 0≤3x≤y≤3) Fxy (x) = f (x). fy (y) 2