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Concept Check: Conditional Quantile 1 point possible (graded) Let (X, Y) be a pair of RVs...
7. Let RVs Yand Yhave the following joint pdf f(x,y)=L if 1 srs2,1Sys2 0, otherwise a)...
7. Let RVs Yand Yhave the following joint pdf f(x,y)=L if 1 srs2,1Sys2 0, otherwise a) Determine the value of k inf(x·y). Plotf(x, y). b) Determine and plot the marginal pdfs fx) and fy) c) Determine PX>1, Y <0 d) Determine the conditional pds, f(xy) and f() xly) arn
Let X and Y be continuous rvs with a joint pdf of the form: ?k(x+y), if(x,y)∈?0≤y≤x≤1?...
Let X and Y be continuous rvs with a joint pdf of the form: ?k(x+y), if(x,y)∈?0≤y≤x≤1? f(x,y) = 0, otherwise (a) Find k. (b) Find the joint CDF F (x, y). 0, otherwise (c) Find the conditional pdfs f(x|y) and f(y|x) (d) Find P[2Y > X] (e) Find P[Y + 2X > 1]
1. Let X and Y be two jointly continuous random variables with joint CDF otherwsie a....
1. Let X and Y be two jointly continuous random variables with joint CDF otherwsie a. Find the joint pdf fxy(x, y), marginal pdf (fx(x) and fy()) and cdf (Fx(x) and Fy)) b. Find the conditional pdf fxiy Cr ly c. Find the probability P(X < Y = y) d. Are X and Y independent?
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....
(Sec 5.1) Suppose the joint pdf of two rvs X and Y is given by $15x2y...
(Sec 5.1) Suppose the joint pdf of two rvs X and Y is given by $15x2y for 0 < x sys1 f(x,y) = 10 otherwise (a) Verify that this is a valid pdf. (b) What is P(X+Y < 1)? (c) What is the probability that X is greater than .7? (Hint: it might help to find the marginal pdf first)
Let X and Y be a random variable with joint PDF: fxx (x, y) = {...
Let X and Y be a random variable with joint PDF: fxx (x, y) = { 1, 2 > 1,0 Sysi 0 otherwise 1. What is a? 2. What is the conditional PDF fy|x(x|y) of Y given X = x? 3. What is the conditional expectation of Ygiven X? 4. What is the expected value of Y?
2. Let X and Y be independent integer-valued RVs with given distributions jezqj = 1. (a) Compute ...
2. Let X and Y be independent integer-valued RVs with given distributions jezqj = 1. (a) Compute the probability P(X = IYI). (b) Compute the probability P(Y/X є Z).
2. Let X and Y be independent integer-valued RVs with given distributions jezqj = 1. (a) Compute the probability P(X = IYI). (b) Compute the probability P(Y/X є Z).
Let X and Y be a random variable with joint PDF: f X Y ( x...
Let X and Y be a
random variable with joint PDF:
f X Y ( x , y ) = { a
y x 2 , x ≥ 1 , 0 ≤ y ≤ 1 0 otherwise
What is a?
What is the conditional PDF of given ?
What is the conditional expectation of given ?
What is the expected value of ?
Let X and Y be a random variable with joint PDF: fxv (, y) = {&, «...
Consider two rvs Xand Ywith joint pdf f(x,y)-k-y, 0<y<x 1 Find the value of the pdf of U=X+ Y evaluated at u = 0.8. Hence, or otherwise, estimate P(0.8<XY<0.801) Consider two rvs Xan...
Consider two rvs Xand Ywith joint pdf f(x,y)-k-y, 0<y<x 1 Find the value of the pdf of U=X+ Y evaluated at u = 0.8. Hence, or otherwise, estimate P(0.8<XY<0.801)
Consider two rvs Xand Ywith joint pdf f(x,y)-k-y, 0
The joint pdf of two continuous RVs X and Y is given by (4e-22–24 0 <...
The joint pdf of two continuous RVs X and Y is given by (4e-22–24 0 < x,y< f(x, y) = { otherwise Then cov(X,Y) equals Hint – Think of the exponent identity eath = eeb and how this can be used to factorize or simplify joint pdf. OO 0.28 0 -0.46 O 0.83 1
7. Let RVs Yand Yhave the following joint pdf f(x,y)=L if 1 srs2,1Sys2 0, otherwise a) Determine the value of k inf(x·y). Plotf(x, y). b) Determine and plot the marginal pdfs fx) and fy) c) Determine PX>1, Y <0 d) Determine the conditional pds, f(xy) and f() xly) arn
1. Let X and Y be two jointly continuous random variables with joint CDF otherwsie a. Find the joint pdf fxy(x, y), marginal pdf (fx(x) and fy()) and cdf (Fx(x) and Fy)) b. Find the conditional pdf fxiy Cr ly c. Find the probability P(X < Y = y) d. Are X and Y independent?
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....
(Sec 5.1) Suppose the joint pdf of two rvs X and Y is given by $15x2y for 0 < x sys1 f(x,y) = 10 otherwise (a) Verify that this is a valid pdf. (b) What is P(X+Y < 1)? (c) What is the probability that X is greater than .7? (Hint: it might help to find the marginal pdf first)
Let X and Y be a random variable with joint PDF: fxx (x, y) = { 1, 2 > 1,0 Sysi 0 otherwise 1. What is a? 2. What is the conditional PDF fy|x(x|y) of Y given X = x? 3. What is the conditional expectation of Ygiven X? 4. What is the expected value of Y?
2. Let X and Y be independent integer-valued RVs with given distributions jezqj = 1. (a) Compute the probability P(X = IYI). (b) Compute the probability P(Y/X є Z).
2. Let X and Y be independent integer-valued RVs with given distributions jezqj = 1. (a) Compute the probability P(X = IYI). (b) Compute the probability P(Y/X є Z).
Let X and Y be a
random variable with joint PDF:
f X Y ( x , y ) = { a
y x 2 , x ≥ 1 , 0 ≤ y ≤ 1 0 otherwise
What is a?
What is the conditional PDF of given ?
What is the conditional expectation of given ?
What is the expected value of ?
Let X and Y be a random variable with joint PDF: fxv (, y) = {&, «...
Consider two rvs Xand Ywith joint pdf f(x,y)-k-y, 0<y<x 1 Find the value of the pdf of U=X+ Y evaluated at u = 0.8. Hence, or otherwise, estimate P(0.8<XY<0.801)
Consider two rvs Xand Ywith joint pdf f(x,y)-k-y, 0
The joint pdf of two continuous RVs X and Y is given by (4e-22–24 0 < x,y< f(x, y) = { otherwise Then cov(X,Y) equals Hint – Think of the exponent identity eath = eeb and how this can be used to factorize or simplify joint pdf. OO 0.28 0 -0.46 O 0.83 1
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