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6. Let the random variables X and Y represent the population of two species/organisms that compete...
. Let X and Y be the proportion of two random variables with joint probability density...
. Let X and Y be the proportion of two random variables with joint probability density function f(x, y)o, elsewhere. (a) Find P(X < 3|Y= 2). (b) Are X and Y independent? Why? (c) Find E(Y/X)
. Let X and Y be the proportion of two random variables with joint probability density...
. Let X and Y be the proportion of two random variables with joint probability density function f(x, y)o, elsewhere. (a) Find P(X < 3|Y= 2). (b) Are X and Y independent? Why? (c) Find E(Y/X)
. Let X and Y be the proportion of two random variables with joint probability density...
. Let X and Y be the proportion of two random variables with joint probability density function f(r, y) e-*, 0, if, 0 < y < x < oo, elsewhere. a) Find P(Xc3.y-2). b) Are X and Y independent? Why? c) Find E(Y/X)
Let X and Y be two independent random variables with X =d R(0, 2) and Y...
Let X and Y be two independent random variables with X =d R(0, 2) and Y =d exp(1). (a) Use the convolution formula to calculate the probability density function of W =X+Y. (b) Derive the probability density function of U = XY .
Let X and Y be two random variables with the joint probability density function: f(x,y) =...
Let X and Y be two random variables with the joint probability density function: f(x,y) = cxy, for 0 < x < 3 and 0 < y < x a) Determine the value of the constant c such that the expression above is valid. b) Find the marginal density functions for X and Y. c) Are X and Y independent random variables? d) Find E[X].
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.
let x and y be two random variables type with pdf f(x,y) = e^(-x-y); 0< x<...
let x and y be two random variables type with pdf f(x,y) = e^(-x-y); 0< x< ∞, 0 <y< ∞, if X+Y = Z then determine p(Z ≤ z) for 0 <z< . Furthermore determine the pdf of Z. (Hint limit of the double integral are 0 <x< z-y and 0<y<z).
5. (a) (6 marks) Let X be a random variable following N(2.4). Let Y be a...
5. (a) (6 marks) Let X be a random variable following N(2.4). Let Y be a random variable following N(1.8). Assume X and Y are independent. Let W-min(x.Y). Find P(W 3) (b) (8 marks) The continuous random variables X and Y have the following joint probability density function: 4x 0, otherwise Find the joint probability density function of U and V where U-X+Y and -ky Also draw the support of the joint probability density function of Uand V (o (5...
13. Let X and Y be continuous random variables with joint density function ( 3 (2...
13. Let X and Y be continuous random variables with joint density function ( 3 (2 - x - y) f(x, y) = { for () < x, y < 2; () < x+y< 2 otherwise. What is the conditional probability P (X < 11Y < 1)?
) Let X, Y be two random variables with the following properties. Y had density function...
) Let X, Y be two random variables with the following
properties. Y had
density function fY (y) = 3y
2
for 0 < y < 1 and zero elsewhere. For 0 < y < 1, given
Y = y, X
had conditional density function fX|Y (x | y) = 2x
y
2 for 0 < x < y and zero elsewhere.
(a) Find the joint density function fX,Y . Be precise about where
the values (x, y) are non-zero....
. Let X and Y be the proportion of two random variables with joint probability density function f(x, y)o, elsewhere. (a) Find P(X < 3|Y= 2). (b) Are X and Y independent? Why? (c) Find E(Y/X)
. Let X and Y be the proportion of two random variables with joint probability density function f(x, y)o, elsewhere. (a) Find P(X < 3|Y= 2). (b) Are X and Y independent? Why? (c) Find E(Y/X)
. Let X and Y be the proportion of two random variables with joint probability density function f(r, y) e-*, 0, if, 0 < y < x < oo, elsewhere. a) Find P(Xc3.y-2). b) Are X and Y independent? Why? c) Find E(Y/X)
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.
5. (a) (6 marks) Let X be a random variable following N(2.4). Let Y be a random variable following N(1.8). Assume X and Y are independent. Let W-min(x.Y). Find P(W 3) (b) (8 marks) The continuous random variables X and Y have the following joint probability density function: 4x 0, otherwise Find the joint probability density function of U and V where U-X+Y and -ky Also draw the support of the joint probability density function of Uand V (o (5...
13. Let X and Y be continuous random variables with joint density function ( 3 (2 - x - y) f(x, y) = { for () < x, y < 2; () < x+y< 2 otherwise. What is the conditional probability P (X < 11Y < 1)?
) Let X, Y be two random variables with the following
properties. Y had
density function fY (y) = 3y
2
for 0 < y < 1 and zero elsewhere. For 0 < y < 1, given
Y = y, X
had conditional density function fX|Y (x | y) = 2x
y
2 for 0 < x < y and zero elsewhere.
(a) Find the joint density function fX,Y . Be precise about where
the values (x, y) are non-zero....
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