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It is a probility question from book “A first course in
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EXAMPLE 2f If the...
Let X and Y be two continuous random variables having the joint probability density 24xy, for...
Let X and Y be two continuous random variables having the joint probability density 24xy, for 0 < x < 1,0<p<1.0<x+y<1 0, elsewhere Find the joint probability density of Z X + Y and W-2Y.
3. Use the proposition in class on independence of two random variables to determine if X...
3. Use the proposition in class on independence of two random variables to determine if X and Y are independent in the following cases (a) The joint PDF of X and Y is fxy(x, y) = 6e-2x=34, 0 < x < 0,0 < y < oo, and zero otherwise. (b) The joint PDF of X and Y is fxy(x, y) = 24xy, for 0 < x +y < 1 and zero otherwise.
1. Suppose the joint density of X and Y is given by f(x,y) = 6e-3x-2y, if...
1. Suppose the joint density of X and Y is given by f(x,y) = 6e-3x-2y, if 0 < x < inf., 0 < y < inf, 0 elsewhere. Part A, Find P( X < 2Y) Part B, Find Cov(X,Y) Part C, Suppose X and Y have joint density given by f(x,y) = 24xy, when 0<= x <=1, 0 <= y <=1, 0 <= x+y <=1, and 0 elsewhere. Are X and Y independent or dependent random variables? why?
The joint probability density function of random variables X and Y is given by f(x,y) ={10xy^2...
The joint probability density function of random variables X and Y is given by f(x,y) ={10xy^2 0≤x≤y≤1,0 otherwise. (a) Compute the conditional probability fX|Y(x|y). (b) Compute E(Y) and P(Y >1/2). (c) Let W=X/Y. Compute the density function of W. (d) Are X and Y independent? Justify briefly.
The joint probability density function of random variables X and Y is given by f(x,y) ={10xy^2 0≤x≤y≤1,0 otherwise. (a) Compute the conditional probability fX|Y(x|y). (b) Compute E(Y) and P(Y >1/2)...
The joint probability density function of random variables X and Y is given by f(x,y) ={10xy^2 0≤x≤y≤1,0 otherwise. (a) Compute the conditional probability fX|Y(x|y). (b) Compute E(Y) and P(Y >1/2). (c) Let W=X/Y. Compute the density function of W. (d) Are X and Y independent? Justify briefly.
2. Random variables X and Y have joint probability density function f(x, y) = kry, 0<<1,0...
2. Random variables X and Y have joint probability density function f(x, y) = kry, 0<<1,0 <y <1. Assume that n independent pairs of observations (C,y:) have been made from this density function. (a) Find the k which makes f(x,y) a valid density function, (b) Find the maximum likelihood estimators of a and B. (c) Find approximate variances for â and B.
1. Consider two random variables X and Y with joint density function f(x, y)-(12xy(1-y) 0<x<1,0<p<1 otherwise...
1. Consider two random variables X and Y with joint density function f(x, y)-(12xy(1-y) 0<x<1,0<p<1 otherwise 0 Find the probability density function for UXY2. (Choose a suitable dummy transformation V) 2. Suppose X and Y are two continuous random variables with joint density 0<x<I, 0 < y < 1 otherwise (a) Find the joint density of U X2 and V XY. Be sure to determine and sketch the support of (U.V). (b) Find the marginal density of U. (c) Find...
QUESTION 4 Suppose Xis a random variable with probability density function f(x) and Y is a...
QUESTION 4 Suppose Xis a random variable with probability density function f(x) and Y is a random variable with density function f,(x). Then X and Y are called independent random variables if their joint density function is the product of their individual density functions: x, y We modelled waiting times by using exponential density functions if t <0 where μ is the average waiting time. In the next example we consider a situation with two independent waiting times. The joint...
Consider two random variables X and Y be the proportion of time that a person travels...
Consider two random variables X and Y be the proportion of time that a person travels to work by bus and MTR respectively (there are other modes as well). Moreover, X and Y has the following joint distribution f(x,y) 24xy, 0 x f(x,y)-0 otherwise 1,0 y 1, x + y 1 () Find the marginal distributions g(x) and h(y) respectively. (ii) Find the conditional density function fxly) (ii Ifit is known that a person has 0.75 chance of using bus,...
Suppose a joint probability density function for two variables X and Y is given as follows:...
Suppose a joint probability density function for two variables X and Y is given as follows: {24x0, if 0 < x < 1,0 < y < 1 f(x, y) = otherwise Please find the probability p (w > 1) =? 3
Let X and Y be two continuous random variables having the joint probability density 24xy, for 0 < x < 1,0<p<1.0<x+y<1 0, elsewhere Find the joint probability density of Z X + Y and W-2Y.
3. Use the proposition in class on independence of two random variables to determine if X and Y are independent in the following cases (a) The joint PDF of X and Y is fxy(x, y) = 6e-2x=34, 0 < x < 0,0 < y < oo, and zero otherwise. (b) The joint PDF of X and Y is fxy(x, y) = 24xy, for 0 < x +y < 1 and zero otherwise.
2. Random variables X and Y have joint probability density function f(x, y) = kry, 0<<1,0 <y <1. Assume that n independent pairs of observations (C,y:) have been made from this density function. (a) Find the k which makes f(x,y) a valid density function, (b) Find the maximum likelihood estimators of a and B. (c) Find approximate variances for â and B.
1. Consider two random variables X and Y with joint density function f(x, y)-(12xy(1-y) 0<x<1,0<p<1 otherwise 0 Find the probability density function for UXY2. (Choose a suitable dummy transformation V) 2. Suppose X and Y are two continuous random variables with joint density 0<x<I, 0 < y < 1 otherwise (a) Find the joint density of U X2 and V XY. Be sure to determine and sketch the support of (U.V). (b) Find the marginal density of U. (c) Find...
QUESTION 4 Suppose Xis a random variable with probability density function f(x) and Y is a random variable with density function f,(x). Then X and Y are called independent random variables if their joint density function is the product of their individual density functions: x, y We modelled waiting times by using exponential density functions if t <0 where μ is the average waiting time. In the next example we consider a situation with two independent waiting times. The joint...
Consider two random variables X and Y be the proportion of time that a person travels to work by bus and MTR respectively (there are other modes as well). Moreover, X and Y has the following joint distribution f(x,y) 24xy, 0 x f(x,y)-0 otherwise 1,0 y 1, x + y 1 () Find the marginal distributions g(x) and h(y) respectively. (ii) Find the conditional density function fxly) (ii Ifit is known that a person has 0.75 chance of using bus,...
Suppose a joint probability density function for two variables X and Y is given as follows: {24x0, if 0 < x < 1,0 < y < 1 f(x, y) = otherwise Please find the probability p (w > 1) =? 3
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