Liniar combinations of random variables 1. Let X and Y be two continuous random variables with joint density function: a. Calculate P(X+Y ≥ !) b. Calculate E(Y-X) c. Calculate Var (Y - X). f(x,y)= 0
Q: Consider the random variables X and Y with joint density function. 0 0.5, Y > 0.5).
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A: Let X and Y be two continuous random variables defined over the sample space S. Then the continuous…
Q: i) Draw a sketch of the area where f(x₁, x₂) is not zero. ii) Find P(X₂ < 1). iii) Find E(X₁X₂).
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A: Solution: From the given information, joint density function of X and Y is
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A: given f(y1,y2) = 6(y12 + y1 . y2/2) /7 , 0<y1<1 ,0<y2<2
Q: i) Draw a sketch of the area where f(x₁, x₂) is not zero. ii) Find P(X₂ < 1). iii) Find E(X₁X₂).
A: The joint PDF is given and first we have to determine the marginal pdf of X2 to find the required…
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A: The conditional probability is defined as : P(X|Y) = P(X,Y=y)P(Y=y)
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A: It is an important part of statistics . It is widely used .
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A: Let X and Y be random variables with the joint density function f(x,y)=x+y, if x,y element of [0,1],…
Q: E (X+ Y)
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A: It is an important part of statistics. It is widely used.
Q: Show E(Y)
A: First we have to determine the marginal pdf of Y to calculate the value of E(Y).
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- 7. Let X and Y be continuous random variables with joint probability density function given by fxy(xy): Sc, (0, 0 < x < y < 1 otherwise a) Find the value of c. b) Find the marginal distributions of X and Y. c) Find the conditional distribution of Y given X. d) Find the E(Y) and Var(Y).The joint density function for a pair of random variables X and Y is f(x, v) = " { S C(x + y) 0 < x < 3, 0 < y< 2 otherwiseLet X and Y be two random variables with joint density function f(x,y) = (3 − x + 2y) / 60, for 1 < x < 3, 0 < y < 5. Is P(X > 2, Y < 3) equal to P(X > 2) × P(Y < 3)?
- The multidimensional random variables H= (c) Let x := 2731 W 21 X2 Yı = follows N₁(μ, E) where 7 3 Y 2 3 Y 6 0 0 5 4 -2 2 4 -2 G (a) Determine all the independent univariate random variables. (b) What is the probability density function for x₁ + 2x₂? [2] tion density function p(y|x) and p(x|y = 1). and y := [₁]. Determine the conditional distribu-7. Let X and Y denote two continuous random variables. Let f(x,y) denote the joint probability density function and fx(x) and fy (y) the marginal probability density functions for X and Y, respectively. Finally let Z = aX + bY, where a and b are non-zero real numbers. (e) Derive an expression for Cov(Z) as a function of Var (X), Var(Y) and Cov(X,Y). [You may use standard results relating to variance and covariance without proof, but these should be clearly stated.]2. Let X and Y denote independent random variables with respective probability density func- tions fx(x) = 2x, 0Show V(Y)Suppose that X and Y are continuous random variables with joint pdf given by c(x²+y?) 03. Let random variables X and Y be independent with joint density fe(x, y). Let Ix (0) and Iy (0) be the Fisher information of X and Y, respectively. Prove that the Fisher information I(x,y)(0) = Ix(0) + Iy(0).Please helpb) Let Y1, Y2.,Y5 be independent random variables with probability density function y 1 e 4 4 f(y)= ,y > 0 ,elsewhere 3 Determine the distribution and parameter of V = EY; using the method of moment i=1 generating function. Hence, find the mean of V using the moment generating function.Find the density of U = Y1 +Y2, where Y1 and Y2 are independent random variables with densities (yı – 1), 3 < Yı < 4, (y2 + 2), 0 < Y2 < 1, fy, (y1) : fy,(y2) = otherwise, otherwise.SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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