Question

Suppose X, Y, and Z are random variables with the joint density function f(x, y, z)...

Suppose X, Y, and Z are random variables with the joint density function

f(x, y, z) = Ce−(0.5x + 0.2y + 0.1z) if x ≥ 0, y ≥ 0, z ≥ 0, and f(x, y, z) = 0 otherwise.

(a) Find the value of the constant C.

(b) Find P(X ≤ 0.75 , Y ≤ 0.5). (Round answer to five decimal places).

(c) Find P(X ≤ 0.75 , Y ≤ 0.5 , Z ≤ 1). (Round answer to six decimal places).

Math   Advanced-Math   
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
Suppose that the random variables  X  and Y  have the following joint probability density function. f ...
Suppose that the random variables  X  and Y  have the following joint probability density function. f (x, y)  =  ce−9x − 7y,    0  <  y  <  x. (a) Find the value of c. (b) Find P(X  <1/6   , Y  <  1)
Suppose that the random variables  X  and Y  have the following joint probability density function. f ...
Suppose that the random variables  X  and Y  have the following joint probability density function. f (x, y)  =  ce−5x − 7y,    0  <  y  <  x. (a) Find the value of c. (b) Find P(X  < 1/3  , Y  <  2)
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...
A joint density function of the continuous random variables x and y is a function f(x,...
A joint density function of the continuous random variables x and y is a function f(x, y) satisfying the following properties. f(x, y) ≥ 0 for all (x, y) ∞ −∞ ∞ f(x, y) dA = 1 −∞ P[(x, y)  R] =    R f(x, y) dA Show that the function is a joint density function and find the required probability. f(x, y) = 1 8 ,   0 ≤ x ≤ 1, 1 ≤ y ≤ 9 0,   elsewhere P(0 ≤...
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
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
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) = xe^−x(y+1), 0 , 0< x < ∞,0 < y < ∞ otherwise (a) Are X and Y independent or not? Why? (b) Find the conditional density function of Y given X = 1.(
Suppose X and Y are continuous random variables with joint density function f(x,y) = x +...
Suppose X and Y are continuous random variables with joint density function f(x,y) = x + y for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. (a). Compute the joint CDF F(x,y). (b). Compute the marginal density for X and Y . (c). Compute Cov(X,Y ). Are X and Y independent?
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 .
7. Suppose that random variables X and Y have a joint density function given by: f(x,...
7. Suppose that random variables X and Y have a joint density function given by: f(x, y) = ? + ? 0 ≤ ?≤ 1, 0 ≤ ? ≤ 1 (a) Find the density functions of X and Y, f(x) and f(y). (b) Find E[X] and Var(Y).
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT