![where (c) is the unit step function: (a) We can write fxy(,y) = [e-*u(x)][2e-2u(y)],? u(x) = 1 { 0 > 1 otherwise Thus, we co](http://img.homeworklib.com/questions/ce5df9e0-e03f-11ea-abb7-cdd0e565918d.png?x-oss-process=image/resize,w_560)
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I am trying to understand why the solution (a) in the second
picture is a valid...
2. Let the random variables X and Y have the joint PDF given below: S 2e-2-Y...
2. Let the random variables X and Y have the joint PDF given below: S 2e-2-Y 0 < x < y < fxy(x,y) = { 0 otherwise (a) Find P(X+Y < 2). (b) Find the marginal PDFs of X and Y. (c) Find the conditional PDF of Y|X = r. (d) Find P(Y <3|X = 1).
2. Let the random variables X and Y have the joint PDF given below: 2e -y...
2. Let the random variables X and Y have the joint PDF given below: 2e -y 0 xyo0 fxy (x, y) otherwise 0 (a) Find P(X Y < 2) (b) Find the marginal PDFs of X and Y (c) Find the conditional PDF of Y X x (d) Find P(Y< 3|X = 1)
I am trying to understand why the conditional PDF f(X|X>1) is what the answer the picture...
I
am trying to understand why the conditional PDF f(X|X>1) is what
the answer the picture indicates given that P(X>1) = 1/e. Should
f(X|X>1) not equal e^(-x-1) instead given the exponential RV is
e^(-x)?
Example 5.20. Let X ~ Exponential(1). (a) Find the conditional PDF and CDF of X given X > 1. (b) Find E[X|X > 1). (c) Find Var(X|X > 1). Solution: (a) Let A be the event that X > 1. Then P(A) = S, ſed 1...
Q2) (20 points) The joint pdf of a two continuous random variables is given as follows:...
Q2) (20 points) The joint pdf of a two continuous random variables is given as follows: < x < 2,0 < y<1 (cxy0 fxy(x, y) = } ( 0 otherwise 1) Find c. 2) Find the marginal PDFs of X and Y. Make sure to write the ranges. Are these random variables independent? 3) Find P(0 < X < 110 <Y < 1) 4) What is fxy(x\y). Make sure to write the range of X.
2. Let the pair (X,Y) have joint PDF fxy(x, y) = c, with 2.2 + y2...
2. Let the pair (X,Y) have joint PDF fxy(x, y) = c, with 2.2 + y2 <1. (a) Find c and the marginal PDFs of X and Y. (b) What are the means of X and Y ? No calculations are needed, only a brief expla- nation is required. (c) Find the conditional PDF of Y given X = x and deduce E|Y|X = x]. (d) Obtain E(XY) and compare it to E[X]E[Y). (e) Are X and Y independent? Explain....
2. Let the random variables X and Y have the joint PDF given below: (a) Find P(X + Y ≤ 2). (b) Find the marginal PDFs o...
2. Let the random variables X and Y have the joint PDF given
below:
(a) Find P(X + Y ≤ 2).
(b) Find the marginal PDFs of X and Y.
(c) Find the conditional PDF of Y |X = x.
(d) Find P(Y < 3|X = 1).
Let the random variables X and Y have the joint PDF given below: 2e -0 < y < 00 xY(,) otherwise 0 (a) Find P(XY < 2) (b) Find the marginal PDFs of...
4. Two random variables X and Y have the following joint probability density function (PDF) Skx 0<x<y<1, fxy(x...
4. Two random variables X and Y have the following joint probability density function (PDF) Skx 0<x<y<1, fxy(x, y) = 10 otherwise. (a) [2 points) Determine the constant k. (b) (4 points) Find the marginal PDFs fx(2) and fy(y). Are X and Y independent? (c) [4 points) Find the expected values E[X] and EY). (d) [6 points) Find the variances Var[X] and Var[Y]. (e) [4 points) What is the covariance between X and Y?
pectively, 3. Ajoint pdf is defined by (C(x + 2y), for 0 <x< 2, and 0...
pectively, 3. Ajoint pdf is defined by (C(x + 2y), for 0 <x< 2, and 0 < y< 1, fx.r(x,y) = -{-4** 0. otherwise. a. Find the value of C. b. Find the marginal pdf of X alone. 9 c. Find the pdf of U = U = x+132 4. Consider n independent rvs XX2, ..., X, having the same distribution with a common variance a?. For any i = 1,2, ..., n, find Cov(x,- 8, 8), where 8 =...
(d) Are X,T,Y,Z are mutually independent? Explain why they are indepedent or why they are not...
(d) Are X,T,Y,Z are mutually independent? Explain why they are
indepedent or why they are not independent.
(e) Find the pdf of K, where K=X+T+Y
1. (10 points) Let f(x, y, z, t) = e-z-y-z-t, x > 0, y > 0, 2 > 0,t > 0, and =0 otherwise, be the joint PDF of (X, Y, Z,T) (a) Compute P{X<Y <T<2} (b) Compute P {X = T = 2 = Y} (c) Compute E[X + 2Y + 32 +T]
1. The joint probability density function (pdf) of X and Y is given by fxy(x, y)...
1. The joint probability density function (pdf) of X and Y is given by fxy(x, y) = A (1 – xey, 0<x<1,0 < y < 0 (a) Find the constant A. (b) Find the marginal pdfs of X and Y. (c) Find E(X) and E(Y). (d) Find E(XY). 2. Let X denote the number of times (1, 2, or 3 times) a certain machine malfunctions on any given day. Let Y denote the number of times (1, 2, or 3...
2. Let the random variables X and Y have the joint PDF given below: S 2e-2-Y 0 < x < y < fxy(x,y) = { 0 otherwise (a) Find P(X+Y < 2). (b) Find the marginal PDFs of X and Y. (c) Find the conditional PDF of Y|X = r. (d) Find P(Y <3|X = 1).
2. Let the random variables X and Y have the joint PDF given below: 2e -y 0 xyo0 fxy (x, y) otherwise 0 (a) Find P(X Y < 2) (b) Find the marginal PDFs of X and Y (c) Find the conditional PDF of Y X x (d) Find P(Y< 3|X = 1)
I
am trying to understand why the conditional PDF f(X|X>1) is what
the answer the picture indicates given that P(X>1) = 1/e. Should
f(X|X>1) not equal e^(-x-1) instead given the exponential RV is
e^(-x)?
Example 5.20. Let X ~ Exponential(1). (a) Find the conditional PDF and CDF of X given X > 1. (b) Find E[X|X > 1). (c) Find Var(X|X > 1). Solution: (a) Let A be the event that X > 1. Then P(A) = S, ſed 1...
Q2) (20 points) The joint pdf of a two continuous random variables is given as follows: < x < 2,0 < y<1 (cxy0 fxy(x, y) = } ( 0 otherwise 1) Find c. 2) Find the marginal PDFs of X and Y. Make sure to write the ranges. Are these random variables independent? 3) Find P(0 < X < 110 <Y < 1) 4) What is fxy(x\y). Make sure to write the range of X.
2. Let the pair (X,Y) have joint PDF fxy(x, y) = c, with 2.2 + y2 <1. (a) Find c and the marginal PDFs of X and Y. (b) What are the means of X and Y ? No calculations are needed, only a brief expla- nation is required. (c) Find the conditional PDF of Y given X = x and deduce E|Y|X = x]. (d) Obtain E(XY) and compare it to E[X]E[Y). (e) Are X and Y independent? Explain....
2. Let the random variables X and Y have the joint PDF given
below:
(a) Find P(X + Y ≤ 2).
(b) Find the marginal PDFs of X and Y.
(c) Find the conditional PDF of Y |X = x.
(d) Find P(Y < 3|X = 1).
Let the random variables X and Y have the joint PDF given below: 2e -0 < y < 00 xY(,) otherwise 0 (a) Find P(XY < 2) (b) Find the marginal PDFs of...
4. Two random variables X and Y have the following joint probability density function (PDF) Skx 0<x<y<1, fxy(x, y) = 10 otherwise. (a) [2 points) Determine the constant k. (b) (4 points) Find the marginal PDFs fx(2) and fy(y). Are X and Y independent? (c) [4 points) Find the expected values E[X] and EY). (d) [6 points) Find the variances Var[X] and Var[Y]. (e) [4 points) What is the covariance between X and Y?
pectively, 3. Ajoint pdf is defined by (C(x + 2y), for 0 <x< 2, and 0 < y< 1, fx.r(x,y) = -{-4** 0. otherwise. a. Find the value of C. b. Find the marginal pdf of X alone. 9 c. Find the pdf of U = U = x+132 4. Consider n independent rvs XX2, ..., X, having the same distribution with a common variance a?. For any i = 1,2, ..., n, find Cov(x,- 8, 8), where 8 =...
(d) Are X,T,Y,Z are mutually independent? Explain why they are
indepedent or why they are not independent.
(e) Find the pdf of K, where K=X+T+Y
1. (10 points) Let f(x, y, z, t) = e-z-y-z-t, x > 0, y > 0, 2 > 0,t > 0, and =0 otherwise, be the joint PDF of (X, Y, Z,T) (a) Compute P{X<Y <T<2} (b) Compute P {X = T = 2 = Y} (c) Compute E[X + 2Y + 32 +T]
1. The joint probability density function (pdf) of X and Y is given by fxy(x, y) = A (1 – xey, 0<x<1,0 < y < 0 (a) Find the constant A. (b) Find the marginal pdfs of X and Y. (c) Find E(X) and E(Y). (d) Find E(XY). 2. Let X denote the number of times (1, 2, or 3 times) a certain machine malfunctions on any given day. Let Y denote the number of times (1, 2, or 3...
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