Let Xand Y be two continuous random variables with joint probability density[3xfunction given by: f(x.y)%D0sysxslelsewherewith E(X) = ECX)- EC) - EC*)= ;and E(XY) = 103E(Y*) = - and E(XY) =;%3DThen the value of the variance of 2X+Y is:O 3/80O 91/32043/3207/20

The given value are EX=34, EX2=35, EY=38, EY2=15 and EXY=310.

Let Xand Y be two continuous random variables with joint probability density 3x function given by: f(x.y)%3D 0sysxsl elsewhere 3. with E(X) =, E(X)=, E(Y) = , E(Y³) = - and E(XY) =- 4 10 Then the value of the variance of 2.X+Y is: O 3/80 O 91/320

Let Xand Y be two continuous random variables with joint probability density 3x function given by: f(x.y)%3D 0sysxsl elsewhere 3. with E(X) =, E(X)=, E(Y) = , E(Y³) = - and E(XY) =- 4 10 Then the value of the variance of 2.X+Y is: O 3/80 O 91/320

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: If X and Y are independent random variables with variances Var(X) = 5 and Var(Y)= (a) find the…

A: Given V(x)=5, V(y)=3, Z=-2x+4y-3 X and Y are independent

Q: Suppose X is a random variable taking values in the interval [0,2] with probability density function…

Q: Suppose X1,..., X15 are iid with pdf f(x) = 3r²,0 < x < 1, zero elsewhere. Let X15 the sample mean.…

A: Given that fx=3x2, 0<x<1 Consider, μ=∫x=01xfxdx =∫x=01x*3x2dx =3x4401 =34 σ2=∫x=01x2fxdx-μ2…

Q: Let X be a continuous random variable with mean μ and standard deviation σ. If X is transformed to Y…

Q: The input voltage to a rectifier is the continuous uniform (-1, 1) random variable U. The rectifier…

Q: Let X and Y be independent standard normal random variables. Determine the pdf of W = x² + y². Find…

A: As per bartleby guidelines we can solve only first question and rest can be reposted

Q: Let X be a Gaussian random variable with zero mean and variance equal to 2. 1-Find the probability…

A: It is given that, X be a Gaussian random variable with zero mean and variance equal to 2. That is,…

Q: Normal distribution. The moment generating function of a random variable U is M(t) = (1 -…

Q: Let X1, X2, X3, X4 be independent random variables of size 4 from a gamma distribution G(a, X) = -1…

A: We want to find the variance of Xi

Q: Let E(X|Y = y) = 3y and var (X|Y = y) = 2, and let Y have the p. d. f. fv) = {e if y > 0 0 otherwise…

A: Given, E[X|Y=y] = 3yVar[X|Y=y] = 2 Find var(X) as follows Var(X) = Var(E[X|Y])…

Q: U is a uniform (0, 1) random variable and X = −ln(1 − U). Find the PDF, CDF of random variable X.…

A: Here, it is provided that a random variable U has uniform distribution over 0,1. Another random…

Q: Let X and Y be two random variables with joint probability mass function: p(x,y) = 1/48 xy(1+y) ???…

A: The provided joint probability mass function is:

Q: Let X ∼ U(a, b). Use the definition of the variance of a continuous random variable (Equation 2.38…

A: The mean of X is given by:

Q: The random variable Y has the Poisson distribution with a mean of 50. (a) What is the variance of Y?…

A: Let Y have a Poisson distribution with a mean of 50.The PMF of Poisson distribution with a mean of…

Q: Let X denote the number of VCRS sold during a random week by a certain store. The probability…

A: Given, xf(x)00.616410.095620.035430.046140.2065Y = 4X+2

Q: Let X and Y be identically distributed with mean 4 and variance 25.(a) If X and Y are uncorrelated,…

A: a) If X and Y are uncorrelated then Cov(X,Y)=0, given V(X)=V(Y)=25 Answer(a): 50

Q: m varia bies 10, 0x2 correlation between 'U' and 'V' is zero, when U = 3 X + 4 Y and V = 3 X- Y.

Q: Let X1 be a normal random variable with mean 2 and variance 3 and let X2 be a no random variable…

A: Given that X1 follows Normal distribution with E(X1)=2 and V(X1)=3. X2 follows normal distribution…

Q: Two zero-mean random variables X and Y have variances o =9 and o = 4. The %3D correlation…

Q: You are analyzing wind velocity v in two dimensions. Assuming that each component vx and vy in…

A: Given, V = VxVy Vx ~ N (0,2)Vy ~ N (0, 2) To find, P (V ≥ 2) = ?

Q: IF it was XG (23) Independent of Xen G (13) Find Miley D-Probability density Function of the…

A: I can definitively solve the question in the image without more information, but I can provide some…

Q: Let X be a random variable and a real number. Show that E(X - a)² = varX + (µ − a)² Hereμ = EX is…

A: E(X−a)2=E(X−μ+μ−a)2=E((X−μ)+(μ−a))2=E((X−μ)2+2(X−μ)(μ−a)+(μ−a)2)=E(X−μ)2+E(2(X−μ)(μ−a))+E(μ−a)2=E(X−…

Q: Let X be a random variable with mean 6.1 and variance 2.4. Let Y be a random variable with mean 7.5…

A: We have given that, E(x)=5.1 , Var(X)=2.4 E(Y)=7.5 , Var(Y)=3.2 , Cov(x,y)=0.65

Q: X and Y are two random variables with variances of and of respectively and r is the coefficient of…

Q: Suppose X and Y are two random variables with covariance Cov(X, Y) = 3 and Var(X) = 16. Find the…

A: The correlation coefficient between two random variables X and Y is defined as: ρ(X, Y) = Cov(X, Y)…

Q: Let X 1 be a normal random variable with mean 2 and variance 3 and let X 2 be a normal random…

Q: If X and Y are any random variables with COV(X, Y) = 0.25, o = 0.36, and o = 0.49, then the…

A: From the given information, Covx,y=0.25 σ2x=0.36 σ2y=0.49 Thus,

Q: Find the variance by calculating the first two moments of the random variable X = (- 1 / λ) ln…

A: For U~u(0,1) pd.f. of U is f(u)= 1, 0<u<1 To find mean and variance we find p.d.f. of X.

Q: Let X, Y N (2, 3) two normal random variables with mean 2 and variance 3. Which of the following…

A: Normal distribution mean , median and mode are eqaul

Q: Suppose X and Y are independent. X has a mean of 1 and variance of 1, Y has a mean of 0, and…

A: According to the Bartleby guidelines expert solve only one question and maximum three subpart of the…

Q: 8. Let y be a normal random variable with a constant mean E(y) = 4, constant variance var(y.) = o?,…

A: We have given that Let yt be a normal random variable E(yt)=μ Var(yt)=σ2 Cov(yt,yj)=0 We have…

Q: Let X and Y be independent random variables with μX = 3, σX = 3, μY = 2, and σY = 3. Find the…

Q: Let X be a random variable distributed as a Normal with mean 0 and variance 2 (i.e., X ~ N(0, 2)).…

Q: Pb (Z = z) = B (8.25z - z2) with z E {1, 2, ......, 5}. Find the mean and variance of Z using…

A: Solution

Q: the joint density: fX,Y(x,y) = 2−x−y, for 0<x<1, 0<y<1 0,…

A: Dear students as per guidelines we answer the first three subparts only.

Q: IF it was XG (23) Independent of Xen G (13) Find Miley D-Probability density Function of the…

A: Sour, The prompt states that X1 follows a Gamma distribution with a shape parameter of 2/3, and X2…

Q: W= X+ 3Y Find the (c) correlations (d) correlation coefficient of V and W

Q: Find the value of Var(X − 2Y + 7).

A: It is given that Var(X)=6, Var(Y)=3 and ρ(X, Y)=-14.

Q: The probability density function of the random variable X is given by 3 a2, 0< < 2 f(x) = otherwise…

Q: Let X1 and X2 be two independent random variables with common mean E(X1) = E(X2) = µ. The variance…

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

Let Xand Y be two continuous random variables with joint probability density
[3x
function given by: f(x.y)%D
0sysxsl
elsewhere
with E(X) = ECX)- EC) - EC*)= ;and E(XY) = 10
3
E(Y*) = - and E(XY) =;
%3D
Then the value of the variance of 2X+Y is:
O 3/80
O 91/320
43/320
7/20

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is Cor(X,Y)=−3/4. Calculate Var(X+Y) with a full explanation
If X is a random variable with pdf f(x) = 2x − 2 where x = (1, 2), find the variance of Y = 2X - 3.
Calculate the variance of a random variable X whose characteristic function is (1+ e3it)² f(t) = 4
The probability distribution of the discrete random variable X is 3-х 3y x = 0,1,2,3. Find the variance of X.
Let X and Y be independent random variables with μX = 3, σX = 3, μY = 2, and σY = 3. Find the mean and variance of X – Y. The mean of X - Y is . The variance of X - Y is .
Let X = (X1, X, )" be a bivariate random variable with variance-covariance matrix 4 -1.5 E(X – E(X))(X – E(X))") = ( -1.5 1 You are given that X1 + aX2 is independent of X1. Find the number a. Give your answer in 2 decimal places. Answer:
Let the random variables X and Y have the joint p.m.f. x+ y f (x, y) = 32 x = 1, 2, y = 1,2,3,4. Find the means lx and uy, the variances oy and oý, and the correlation coefficient p. Are X and Y independent or dependent? 6.
Suppose that X, Y and Z are independent. The expected value is given by E(X) = 0, E(Y) = 1, E(Z) = 5 We also know that the variance is given by Var(X)=1, Var(Y)=1, Var(Z)=25 The values of the covariance are Cov(X,Y)=2, Cov(Y,Z)=1 Which of the satements are true? 1. Cov(ex,Y2 + 1) = 0 2. Е(XY)-1 3. If a and b are real numbers then Cov(aX+bZ, Y+Z)=2a+25b 4. Cov(X,Y)=0
Suppose that y, is an independent response variable (i = 1.....n) with mean, such that g(i) = n₁ = X₁B, where g(.) is a link function, X, is a vector of covariates and 3 is a px 1 vector of coefficients. Let the variance of y; be Var (Y) = V(i), where V(.) is a known function and is a scale parameter. Given: Zi= g'(pi) (Yi - Pi) + Ni w₁ = [V (pi) (g'(pi))²]-¹ 8 where g'(μ) = 9(μ) (a) Show that E(Z₁) = X₂B (b) Show that Var (Z₁) = w¹o. (c) Estimate 3 by minimizing Σ, wi( E(Z₁))² with respect to 3. After you found 8, find the Var(8) and E(3). What do you conclude?
Let X be a Gaussian RV on with expected value (mean) E[X] = 1, Var[X] = 1. Let Y = -3(X-1). Compute the expected value of Y. QUESTION 7 Let X be a Gaussian RV on with expected value (mean) E[X] = 1, Var[X] = 1. Let Y = -3(X-1). Compute the variance of Y.
Calculate E{X}, E{Y }, Var{X}, Var{Y } and ρ XY for random variables X and Y with jointdensity function
* Let E(X]Y = y) = 3y and var(X|Y = y) = 2, and let Y have the p. d. f. se-y if y > 0 fG) = {o otherwise Then the variance of X is