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Please provide correct answer (Very Important) Consider the following joint probability distribution: y fxY (x, y)...
Consider joint probability distribution given below y fxy (x, у) х 1.0 1 11/32 1/32 1.5 2 1.5 1/4 2.5 4 1/4 3.0 1/8 Determine the following: In your intermediate calculations, round all fractions to three decimal places. Round your answers to three decimal places (e.g 98.765) (a) Conditional probability distribution of Y qiven that X = 1,5. у Fуus 0) 1 2 3 5 (b) Conditional probability distribution of X given that Y 2. 1.0 1.5 2.5 (c) E(YIX...
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...
1. Consider the joint distribution fXY (x, y) = k · x y (1) over the domain 0 < x < 1, 0 < y < 1, for some k > 0. (a) What value should k have for f to be a proper density? (b) Find the marginal densities of X and Y . Hint: x y = exp[y · log(x)]. (c) Find the mean of Y . (d) Find the conditional mean of Y , given X
a. Given the joint probability den- sity function fxy(x, y) as, Skxy, (x, y) e shaded area Jxy(, 9) = 10 otherwise Find [i] k [ii] fx(x) [iii] fy(y) Are X and Y independent? b. Given the joint probability density function fxy(x, y) as, fxy(x, y) = { 0 kxy, (x, y) E shaded area otherwise Find [i] k [ii] fx(x) [iii] fy(y) Are X and Y independent? 2 1
Q1. [4+2+4 marks] Consider the following joint probability distribution fxy(x, y). 2 4 0.05 0.1 0,05 0.02 0.1 0.05 2 0.02 0.13 0.3 0.01 0.02 0.15 a) Find the covariance between X and Y b) Are X and Y independent? Explain. c) Find V(X12).
1. (25 points) Consider the following probability density function and the random vector W. fxy(x,y)= 1/16 0 |x|52, lyls2 elsewhere X W=(x,y)" Li a) (5 points) Find and plot the conditional joint probability density function f wilx<0,y>o)(W|x<0, y>0) b) (5 points) Find and plot the conditional joint cumulative distribution function Fw1(x<0,y>0)(W|x<0, y>0) c) (5 points) Find E(W). d) (10 points) Find E(W x<0, y>0).
If the joint probability distribution of X and Yis given by: fxy)-2xty48,for all x-0,1,2,3 and y-0,1,2 Determine Part a: P(Xs3,Y-1) Part b: P(X+Y-4) Part c: Part d: E(XY)]
Exercises: 1) The joint distribution of X and Y is given by the following table: y 1.5 2 fxy(x, y) 1/4 1/8 1/4 1/4 1/8 Compute: a) P(X=1.5, Y =2). b) P(X=1, Y =2). c) P(X=1.5). d) P(X<2.5, Y<3) e) P(Y>3) f) E(X), E(Y), V(X) and V(Y). g) The marginal distributions of X and of Y. h) Conditional probability distribution of Y given that X = 1.5. i) E(Y|X=1.5) j) E(XY) k) Are X and Y independent? Explain why or...
Consider fx (x)=e*, 0<x and joint probability density function fx (x, y) = e) for 0<x<y. Determine the following: (a) Conditional probability distribution of Y given X =1. (b) ECY X = 1) = (c) P(Y <2 X = 1) = (d) Conditional probability distribution of X given Y = 4.
3. Consider the joint probability distribution for Y and X. X/Y 2 4 6 1 0.2 0.21 2 10 201 3 5.2 0 2 a) Calculate the marginal densities for both Y and X. b) Show using the conditional distribution for Y and the marginal distribution for Y, that X and Y are not independent. c) Calculate the E(Y|x = 1)and V(Y | x = 1).