Question

Compound probability density function of random variables x and ? ??, ? (?, ?) = {...

Compound probability density function of random variables x and ? ??, ? (?, ?) = { 6/7 (?*2 + ??/2), 0 <? <2, 0 <? <1

(? ,  other It is given as.

According to this

(a) Show that this function is a probability density function.

(b) Find the marginal probability density function of ?.

(c) Calculate the probability ? {?> ?}.

(d) Find the expected value of ? [?].

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Compound probability density function of random variables ? and ? ??, ? (?, ?) = (6/7...
Compound probability density function of random variables ? and ? ??, ? (?, ?) = (6/7 (? * y + (? * ?) / 2), 0 <? <2, 0 <? <1?, other It is given as. According to this (a) Show that this function is a probability density function. (b) Find the marginal probability density function of ?. (c) Calculate the probability ? {?> ?}. (d) Find the expected value of ? [?].
a) The joint probability density function of the random variables X, Y is given as f(x,y)...
a) The joint probability density function of the random variables X, Y is given as f(x,y) = 8xy    if  0≤y≤x≤1 , and 0 elsewhere. Find the marginal probability density functions. b) Find the expected values EX and EY for the density function above c) find Cov  X,Y .
Suppose that the joint probability density function of the random variables X and Y is f(x,...
Suppose that the joint probability density function of the random variables X and Y is f(x, y) = 8 >< >: x + cy^2 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 0 otherwise. (a) Sketch the region of non-zero probability density and show that c = 3/ 2 . (b) Find P(X + Y < 1), P(X + Y = 1) and P(X + Y > 1). (c) Compute the marginal density function of X and Y...
15.1The probability density function of the X and Y compound random variables is given below. X                         &nbsp
15.1The probability density function of the X and Y compound random variables is given below. X                                        Y 1 2 3 1 234 225 84 2 180 453 161 3 39 192 157 Accordingly, after finding the possibilities for each value, the expected value, variance and standard deviation; Interpret the asymmetry measure (a3) when the 3rd moment (µ3 = 0.0005) according to the arithmetic mean and the kurtosis measure (a4) when the 4th moment (µ4 = 0.004) according to the arithmetic...
Problem 4 The joint probability density function of the random variables X, Y is given as...
Problem 4 The joint probability density function of the random variables X, Y is given as f(x,y)=8xy if 0 ≤ y ≤ x ≤ 1, and 0 elsewhere. Find the marginal probability density functions. Problem 5 Find the expected values E (X) and E (Y) for the density function given in Problem 4. Problem 7. Using information from problems 4 and 5, find Cov(X,Y).
Q1) The joint probability density function of the random variables X and Y is given by...
Q1) The joint probability density function of the random variables X and Y is given by ??,? (?, ?) = { ?, 0 < ? < ? < 1 0, ??ℎ?????? a) Find the constant ? b) Find the marginal PDFs of X and Y. c) Find the conditional PDF of X given Y, i.e., ?(?|?) d) Find the variance of X given Y, i.e., ???(?|?) e) Are X and Y statistically independent? Explain why.
Let X and Y be two continuous random variables with joint probability density function f(x,y) =...
Let X and Y be two continuous random variables with joint probability density function f(x,y) = 6x 0<y<1, 0<x<y, 0 otherwise. a) Find the marginal density of Y . b) Are X and Y independent? c) Find the conditional density of X given Y = 1 /2
4. Let X and Y be random variables having joint probability density function (pdf) f(x, y)...
4. Let X and Y be random variables having joint probability density function (pdf) f(x, y) = 4/7 (xy − y), 4 < x < 5 and 0 < y < 1 (a) Find the marginal density fY (y). (b) Show that the marginal density, fY (y), integrates to 1 (i.e., it is a density.) (c) Find fX|Y (x|y), the conditional density of X given Y = y. (d) Show that fX|Y (x|y) is actually a pdf (i.e., it integrates...
The joint probability density function of two random variables (X and Y) is given by fX,Y...
The joint probability density function of two random variables (X and Y) is given by fX,Y (x, y) = ( C √y (y ^(α+1)) exp {( − y(2β+x ^2 ) )/2 } , x ∈ (−∞,∞), y ∈ [0,∞), 0 otherwise. (a) Find C. (b) Find the marginal density of Y . What type of distribution does Y follow? (c) Find the conditional density of X | Y . What type of distribution is this?
For continuous random variables X and Y with joint probability density function. f(x,y) = xe−(x+y) when...
For continuous random variables X and Y with joint probability density function. f(x,y) = xe−(x+y) when x > 0 and y > 0 f(x,y) = 0 otherwise a. Find the conditional density F xly (xly) b. Find the marginal probability density function fX (x) c. Find the marginal probability density function fY (y). d. Explain if X and Y are independent
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT