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LSM 3 Part A. Let X, Y be two exponential (2) random variables that are independent from each other. We know that X should have DF of x)for 20 and CDF of F)for20. 1. (5 credits) Let I-min(X, . Obt...
so ive been stuck for a good while and i tried an attempt but im so lost. Im wondering what im doing wrong LSM 3 Part A. Let X, Y be two exponential (A) random variables that are - e for x20 1....
so ive been stuck for a good while and i tried an attempt but
im so lost. Im wondering what im doing wrong
LSM 3 Part A. Let X, Y be two exponential (A) random variables that are - e for x20 1. (5 credits) Let IminX . Obtain the PDE 2. (5 credits) Let A be the event iXY. Obtain the conditional joint PDE of 3*. (10 credits) Let W-Y-X. Obtain the conditional PDF of fwwlA) PlA)
LSM 3...
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?
Let X and Y be independent exponential random variables with pdfs f(x) = λe-λx (x >...
Let X and Y be independent exponential random variables with pdfs f(x) = λe-λx (x > 0) and f(y) = µe-µy (y > 0) respectively. (i) Let Z = min(X, Y ). Find f(z), E(Z), and Var(Z). (ii) Let W = max(X, Y ). Find f(w) (it is not an exponential pdf). (iii) Find E(W) (there are two methods - one does not require further integration). (iv) Find Cov(Z,W). (v) Find Var(W).
33. Let X and Y be independent exponential random variables with respective rates λ and μ. (a) Argue that, conditio...
33. Let X and Y be independent exponential random variables with respective rates λ and μ. (a) Argue that, conditional on X> Y, the random variables min(X, Y) and X -Y are independent. (b) Use part (a) to conclude that for any positive constant c E[min(X, Y)IX > Y + c] = E[min(X, Y)|X > Y] = E[min(X, Y)] = λ+p (c) Give a verbal explanation of why min(X, Y) and X - Y are (unconditionally) independent.
33. Let X...
Let X and Y be independent exponential random variables with parameter 1. Find the joint PDF...
Let X and Y be independent exponential random variables with parameter 1. Find the joint PDF of U and V. U = X + Y and V = X/(X + Y)
(25 points,) Let X and Y be two independent and identically distributed random variables that have exponential distribution with rates 1 respectively. Find the distribution of Note: you can give eith...
(25 points,) Let X and Y be two independent and identically distributed random variables that have exponential distribution with rates 1 respectively. Find the distribution of Note: you can give either cdf or pdf)
(25 points,) Let X and Y be two independent and identically distributed random variables that have exponential distribution with rates 1 respectively. Find the distribution of Note: you can give either cdf or pdf)
Let X and Y be independent exponential random variables with pa- rameter ? = 1. Given...
Let X and Y be independent exponential random variables with pa- rameter ? = 1. Given that X and Y are independent, their joint pdf is given by the product of the individual pdfs of X and Y , that is, fX,Y(x, y) = fX(x) fY(y). The joint pdf is defined over the same set of x-values and y-values that the individual pdfs were defined for. Using this information, calculate P (X ? Y ? 2) where you can assume...
(15 points) Consider two independent, exponential random variables X,Y ~ exp(1). Let U = X +...
(15 points) Consider two independent, exponential random variables X,Y ~ exp(1). Let U = X + Y and V = X/(X+Y). (a) (5 points) Calculate the joint pdf of U and V. (b) (5 points) Identify the distribution of U. If it has a "named” distribution, you must state it. Otherwise support and pdf is enough. (c) (5 points) Identify the distribution of V.If it has a "named” distribution, you must state it. Otherwise support and pdf is enough.
4. Let X and Y be independent exponential random variables with pa- rameter ? 1. Given...
4. Let X and Y be independent exponential random variables with pa- rameter ? 1. Given that X and Y are independent, their joint pdf is given by the product of the individual pdfs of X and Y, that is, fxy(x,y) = fx(x)fy(y) The joint pdf is defined over the same set of r-values and y-values that the individual pdfs were defined for. Using this information, calculate P(X - Y < t) where you can assume t is a positive...
A) Let X and Y be two random variables with known joint PDF Ir(x, y). Define two new random varia...
a) Let X and Y be two random variables with known joint PDF Ir(x, y). Define two new random variables through the transformations W=- Determine the joint pdf fz(, w) of the random variables Z and W in terms of the joint pdf ar (r,y) b) Assume that the random variables X and Y are jointly Gaussian, both are zero mean, both have the same variance ơ2 , and additionally are statistically independent. Use this information to obtain the joint...
so ive been stuck for a good while and i tried an attempt but
im so lost. Im wondering what im doing wrong
LSM 3 Part A. Let X, Y be two exponential (A) random variables that are - e for x20 1. (5 credits) Let IminX . Obtain the PDE 2. (5 credits) Let A be the event iXY. Obtain the conditional joint PDE of 3*. (10 credits) Let W-Y-X. Obtain the conditional PDF of fwwlA) PlA)
LSM 3...
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?
33. Let X and Y be independent exponential random variables with respective rates λ and μ. (a) Argue that, conditional on X> Y, the random variables min(X, Y) and X -Y are independent. (b) Use part (a) to conclude that for any positive constant c E[min(X, Y)IX > Y + c] = E[min(X, Y)|X > Y] = E[min(X, Y)] = λ+p (c) Give a verbal explanation of why min(X, Y) and X - Y are (unconditionally) independent.
33. Let X...
(25 points,) Let X and Y be two independent and identically distributed random variables that have exponential distribution with rates 1 respectively. Find the distribution of Note: you can give either cdf or pdf)
(25 points,) Let X and Y be two independent and identically distributed random variables that have exponential distribution with rates 1 respectively. Find the distribution of Note: you can give either cdf or pdf)
(15 points) Consider two independent, exponential random variables X,Y ~ exp(1). Let U = X + Y and V = X/(X+Y). (a) (5 points) Calculate the joint pdf of U and V. (b) (5 points) Identify the distribution of U. If it has a "named” distribution, you must state it. Otherwise support and pdf is enough. (c) (5 points) Identify the distribution of V.If it has a "named” distribution, you must state it. Otherwise support and pdf is enough.
4. Let X and Y be independent exponential random variables with pa- rameter ? 1. Given that X and Y are independent, their joint pdf is given by the product of the individual pdfs of X and Y, that is, fxy(x,y) = fx(x)fy(y) The joint pdf is defined over the same set of r-values and y-values that the individual pdfs were defined for. Using this information, calculate P(X - Y < t) where you can assume t is a positive...
a) Let X and Y be two random variables with known joint PDF Ir(x, y). Define two new random variables through the transformations W=- Determine the joint pdf fz(, w) of the random variables Z and W in terms of the joint pdf ar (r,y) b) Assume that the random variables X and Y are jointly Gaussian, both are zero mean, both have the same variance ơ2 , and additionally are statistically independent. Use this information to obtain the joint...
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