2. Let the independent random variables X1 and X2 have Bin(0.1,2) and Bin(0.5, 3), respectively. d. Find V ar(X1 +X2).

Q: If X and Y are two independent random variables such that E[X]=2, variance of X = o}, E[Y]= 1, and…

A:

Q: ssume that X and Y are random variables with the following parameters: = 13, ly 12, оъ 3 4 апd oy 3,…

A: Solution: Given information: μx= 13 μy= 12 σx= 4σy=3and σxy=0.8

Q: Let X be a random variable such that E(X2m) = (2m)!/(2mm!), m =1, 2, 3, . . . and E(X2m−1) = 0, m =…

A:

Q: Q1. Suppose that X and Y are jointly continuous random variable - x for 0 < x < 1 and 1 < y < 2 f(x,…

A: As per our company guidelines we are supposed to  answer only first 3 subparts. kindly repost other…

Q: We have the following information about the random variables X and Y: 1.5, мү – 1.5 , ox . 2, σΥ…

A:

Q: Let x and y be two independent N(0, 1) random variables and Z = 1+ X + XY², W = 1+ X. Find Coy(7,W).

A:

Q: (A) ơy = 0xı + Ox2 Vox1 + Ox2 +o? = Ox1 +0x2 (B ) συ .2 (C) oy = -2 x2 X1 .2 -2 (D) Oy/y = X2

A: The standard deviation is not directly added together but the variance is added for variables. So…

Q: 2. Let Z1,..., Z, be i.i.d. standard normal random variables and define X = Z;, k = 1,..., n. j=1…

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Q: Show that if X € N(0,1) and Y e x2(n) ables, then X/VY/n E t(n). are independent random vari-

A: Given information: The random variable X follows normal distribution with mean 0 and variance 1.…

Q: 2. Let X and Y be random variables such that V(X) = V(Y). Show that Cov(X + Y, X - Y) = 0.

A: we have given that  V(X)=V(Y) and C(X,Y)=C(Y,X)   ,C(X,X)=V(X) ,  C(Y,Y)=V(Y)

Q: Suppose that X, and X2 are aiscrete random variables with joint pdf of the form f(x1,x2) = c(x1 +…

A:

Q: Let X and Y be two random variables such that E(X)=1, E(Y) =3, X, =3X-2 and Y = 2Y +1. If…

A: Given  E(X)=1 , E(Y)=3 , Cov(X1,Y1)=-1 X1=3X-2 , Y1=2Y+1 Hence option (d) is correct choice and the…

Q: Suppose x is a random variable with deneity function given by: (kx 0sxs1 f(x)=- otherwise Compute…

A:

Q: Let X be a continuous random variable with domain D = [0, 7] and PDF 0 <x < 2, 2<r < 5, 2a

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Given: X and Y are random variables with PI,Y -.75, o = 96, and Oy = 114. %3D a) Draw a rough…

A: Cov(x,y) =ρx,yσx×σy=-0.7596×114=-8208

Q: Let the random variable X and Y have the joint p.d.f. [12xy(1-x) f(x,y)= 0 Find E[X] and Variance o…

A: Given f(x,y) = 12xy(1-x)    0&lt;x&lt;1     0&lt;y&lt;1

Q: Let X be a random variable with p.d.f. 2e-2x 0<x<00 f (x) =• , find E(e 2*) O.w

A: Given, the probability distribution function of a random variable X- fx=2e-2x  ; 0&lt;x&lt;∞0…

Q: Suppose X, Y and Z be random variables with j.p.m. f. f(x, y, z)= kxyz with x E {1,2}, y = {1, 2,…

A: Given information: The value of k is obtained below:

Q: (30) Let X be a random variable with p.d.f. 2e-2x 0<x<0 f(x) = { , find E(e*) O.w

A: It is given X is a random variable with pdf f(x) = 2e-2x,0&lt;x&lt;∞0,otherwise

Q: Exercise 28 Let X - Binom(16, ) and Y ~ Geom() be two independent random variables. Compute (i) E(X…

A: As by company policy I have solved first three part of this question....

Q: Let X and Y be two (continuous or discrete) random variables with E(X)=D2, E(Y)3D5, Var(X)=9,…

A: Given: E(X) = 2 E(Y) = 5 Var(X) = 9 Var(Y) = 16 Cov(X,Y) = 5 Formula Used: Var(X-Y) = V(X) - V(Y) -…

Q: If X and Y have the joint probability distributionf(−1, 0) = 0, f(−1, 1) = 1 4 , f(0, 0) = 16 , f(0,…

A: The joint probability distribution of the random variables is given as follows:

Q: For the discrete random variable X, P(X = 1) = p = 1 – P(X = -1). Please find c so as to be E(cX) =…

A:

Q: Let X1 - b(n1, p) and X2 ~ b(n2, p) be independent random variables. a) Find the m.g.f. of Y = X1+…

A: Given that X1 follows b(n1, p) and X2 follows b(n2, p) and they are independent.

Q: Let X and Y be two jointly continuous random variables. Let Z = X +Y. Show that F2(=) = FxIr(V=- v°…

A:

Q: Let Y₁ 1 X=(x,-X₂), where X, and X₂ are independent random variables and each of them is distributed…

A: Given that the independent random variables X1 and X2 follows χ22 distribution.

Q: || f(x,y)dxdy = 1 if X and Y are discret random variable

A: The objective is to state whether the statement is true or false. ∫-∞∞∫-∞∞fx,ydxdy=1  if X and Y are…

Q: Let X1, X2, X3 form a random sample from U(0,1). Find a- The distribution of the second order…

A:

Q: Let X and Y be random variables. Suppose Var(X) = 1.6, Var(Y) = 1.5, and Cov(X, Y) = 0.1. Let Z =…

A: Solution: From the given information, Var(X) =1.6, Var(Y) =1.5 and Cov (X, Y) =0.1. Let Z =…

Q: Let X be a random variable with p.d.f. ((k +4)(x+2) f (x) ={ 0<x<2 , find (1) k (2) E(x) O.W

A: (a) We know, ∫fx dx=1∫02k+4x+2 dx=1∫02kx+2k+4x+8 dx=1kx22+2kx+2x2+8x02=12k+4k+8+16=16k=-23k=-236

Q: Let X be a random variable with p.d.f. 1<x<0 f(x) =- find k. O.W

A: Given, X be a random variable with p. d. f. f(x)=12kx-2   ; 1&lt;x&lt;∞0           ; O.W. constant k…

Q: Let X, Y and Z be three independent random variables such that E(X)-E(Y)=E(Z)=1 and…

A: Solution: Given, E(X)=E(Y)=E(Z)=1 E(X^2)=E(Y^2)=E(Z^2)=10

Q: Suppose (X,Y) is a continuous random variables with joint probability d 4xy Osxs1,0sys1 x,Mx.v) = {"…

A: Let X be a random continuous variable with probability density function(pdf) f(x) then the expected…

Q: If X is a continuous random variable and y = aX + b Prove that E ( Y ) = a E ( X ) + b and V (Y) =…

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Q: Suppose we have three independent random variables X, Y and Z where... Var(X + 2Y) = 13, Var(2Y +…

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Q: H/W: if X and Y are continuous random variables, prove E[X] = E[E[X|Y]]? %3D

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Q: Two random variables Z and W are defined as Z = X + aY and W = X - aY, where X and Y are also random…

A:

Q: Let X1 and X2 be independent random variables for which P(Xi = 1) = 2/5 and P(Xi = 2) = 3/5 . Define…

A: Correlation Coefficient between two Random Variables: If X and Y be two random variables, then the…

Q: 2x Verify that f(x) for x=0,1,2,.k can serve as a pmf of a random variable X. %3D k(k +1)

A: Solution: 7. From the given information,

Q: Q1: Let X1, X2~iid U(0,1), find the probability that the random interval 3X2' X2 includes . 3

A:

Q: Consider a multivariate random variable (X1, X2, X3) with parameters T1 = 0.4; T2 = 0.1; T3 =0.5;…

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Q: e Prove that E(X) independent. E(X/Y), where X and Y are two random variables which are %3D

A:

Q: Let X1,..., Xn an iid random sample from Gamma(a, X). Show that [I-1 X; and E X; are jointly…

A: Given:  random variables Xi (i=1,2,....n) are iid from gamma(α,λ) then to show that ∏Xi and ∑Xi  is…

Q: c) Suppose that X and Y are jointly continuous random variable for 0 <x <1 and 1< y< 2 f(x, y) = {%*…

A: From the given information, the joint probability density function of X and Y is,

Q: Let X be a random variable with p.d.f. 2e-2x 0< x<00 f(x) = , find E(x). O.w

A: We know that, E(x)= integration |x X*f(x) dx

Q: Let X and Y be independent random variables distributed as N(-1, 1) and N(1, 1), respectively. Find…

A: Given: X follows a  normal distribution with mean -1 i.e. µ= -1 and the standard deviation of 1 i.e.…

Q: Assume that X and Y are random variables with the following parameters: - 4 and oy 3, 13, Hy 12, Ох…

A:

Q: 4. Let X, Y be independent random variables. Prove that E(XY) = E(X) E(Y) and hence show that V(X…

A: The expected value is also known as average of the probability distribution function. It is the…

Q: Let X and Y be jointly normal random variables with parameters µx = -1, ož = 1 4, µy = 1, o? 1 and p…

A: μX = -1  μY = 1 σX2 = 4 σY2= 1 ρ=12 (a) Find PX+3Y &lt; 4 (b) Find E(X2Y2)

Q: Consider two jointly random variables, X and Y with joint PDF f(x,y) = {de-2x-3y, x, y ≥ 0 otherwise…

A: Given  A joint distribution using two jointly random variables. We need to calculate the…