2) Let G and H be two independent unbiased estimators of θ. Assume that the variance of G is two times the variance of H. Find the constants a and b so that aG + bH is an unbiased estimator with the smallest possible variance for such a linear combination.

Q: Refer to question (a). Find the mean of X and the variance covariance matrix of X, where X = (X1,…

A: The moment generating function(MGF) of a random variable defines the moments of a random variable.…

Q: Let X and Y be independent random variables, each with mean=mu and variance=sigma^2. Find the…

A: From the given information, Consider, X and Y be independent random variables,…

Q: p(x) Compute E(X), E(X²), and V(X). x ft3 (X) = x²) = (X) = If the price of a freezer having…

A: Since the question has multiple sub parts we will solve the first three sub parts. Please resend the…

Q: Let X and Y be independent random variables with means ux, μy and variances o, oy. Find an…

A: Given:  Random variable x and y are independent with means ux, uy  , varience σ2(x) and σ2(y)  E(x)=…

Q: A variable with a population average of 50 and a variance of 100 is likely to have an average…

A:

Q: .Determine the F statistics (write the result in X.XX) 12. Determine the critical value, F for alpha…

A: Route25 (X) Interstate (Y) (x-xbar)^2 (y-ybar)^2 52 59 39.5102 0 67 60 75.93878 1 56 61…

Q: hemical supply company currently has in stock 100 lb of a certain chemical, which it sells to…

A: Given: x 1 2 3 4 p(x)       0.3     0.5     0.1     0.1

Q: If X is a Poisson variable such that P(X = 2) = 9P(X = 4) +90 P(X = 6), %3D %3D %3D find the mean…

A: Both the above given questions are same I am giving Answer one of them.

Q: If X is a Poisson variable such that P(X= 2) = 9P(X = 4) + 90P(X=6), find the mean and variance of…

A: Let X be the random variable from Poisson distribution  with P(X=2) = 9P(X=4) + 90P(X=6)  Then,  We…

Q: 2. Let X1 and X, be independent random variables with mean u and variance o?. Suppose that we have…

A:

Q: 2,...,A3 a populati ng meanu and variance Which of the estimators have a variance of u? X1+X2++X7 7…

A: Solution

Q: Now, consider an estimator of μ: W=1/16Y1+1/16Y2+1/4Y3+1/8Y4+1/2Y5 This is an example of a…

A: From the given information, W=1/16Y1+1/16Y2+1/4Y3+1/8Y4+1/2Y5 Consider,…

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

A:

Q: If X and Y are independent random variables with variances σ2 X = 5 and σ2 Y = 3, find the variance…

A: Given:VX=5 and VY=3

Q: Two stocks, X and Y, have expected returns ux = 9% and uy = 7% and with standard deviations ox =…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Consider a random sample Y1,Y2, ., Y, from a population with mean µ and variance ơ². Calculate the…

A: Given that Y1, Y2,....,Yn from a population with mean μ and variance σ2. M^=1197Y4+3Y5+7Y7+2Y19…

Q: A chemical supply company currently has in stock 100 Ib of a certain chemical, which it sells to…

A:

Q: If X. Y and Z are uncorrelated RVs with zero means and standard deviations 5 12 and 9 respectively…

A: Given  X,Y and Z are uncorrelated, which mean cov(X,Y)=Cov(Y,Z)=Cov(X,Z)=0  E(X)=E(Y)=E(Z)=0…

Q: 20. The lines of regression of y on x and x on y are, respectively, y= x+ 5 and 16x -9y 94. Find the…

A:

Q: Y is a random variable and "a" and "b" two real constants. Without resorting to the properties of…

A: Given that, Y is a random variable and "a" and "b" two real constants. Without resorting to the…

Q: The management of a supermarket wants to adopt a new promotional policy of giving free gift to every…

A: Given data,Mean μ=400variance σ2=900sd σ=30P(X<x)=12%=0.12x=?

Q: Consumer demand for milk in a certain locality, per month, is known to be a general Gamma (Erlang)…

A:

Q: Suppose that you have to choose an optimal portfolio from a list of n stocks. Stock i has expected…

A: Given: A list of n stocks Stock i has expected revenue rate μi with variance σi2 for i=1,2,...,n…

Q: For the joint pdf of Exercise 30 in Chapter 4 (page 170): (a) Find the correlation coefficient of X…

A: (a). Determine the correlation coefficient of X and Y: The probability density function is given…

Q: Find a such that aY is an unbiased statistic for 0 and find its variance. (Note that the roles of X…

A:

Q: Derive the mean and he variance of X ~ Beta Ca, f).

A:

Q: Let X, and X be two identically distributed random variables with a correlation coefficient equal to…

A: First, we need to find the covariance of X1  and X2 from their correlation coefficient,

Q: Let X1 and X2 be two independent random variables with the same mean µ and the sar variance o?.…

A: 1.   Let X1, X2 be two independent random variables with the same mean µ and the same variance σ2.…

Q: Suppose that X ~ Pareto(7). Define Y = In(X+1). If E[X] = }, then what is the variance %3D of Y?

A: The probability density function(pdf) for a random variable X~Pareto(γ) is given by fX(x)=γ(1+x)γ+1,…

Q: A chemical supply company currently has in stock 100lb of a certain chemical, which it sells to…

A: We have given that,  X be the random variable having probability mass function (p.m.f),    X   :-…

Q: Then the value of the variance of X+Y is:

A: Variance of X + Y can be calculated as V(X + Y) = V(X) + V(Y) + 2Cov(X, Y)

Q: Let Y1, Y2, Y3, Y4, and Y, be i.i.d. random variables from a population with mean u and variance o?.…

A: given data let y1,y2,y3,y4 and y5 be random variablesand givenW=18y1+18y2+15y3+15y4+720y5

Q: Find the variance of X + 3Y + Z + 6 in terms of the variances and covariances of X, Y, and Z.

A: Given:  X + 3Y + Z + 6

Q: Consider an estimator of μ: W= 1/6 Y1+1/16Y2+1/4Y3+1/8Y4+1/2Y5 This is an example of a weighted…

A: Estimation and Estimator: When we are concerned in finding numerical values of unknown parameter(s),…

Q: Let X1,X2 denote the variables for the two-dimensional data in Exercise 1. Find a new variable yl of…

A:

Q: 4) Find the variance V(X).

A:

Q: Suppose X and Y are two independent variables with variance 1. Let Z = X+bY where b > 0. If Cor(Z, Y…

A: Given that, V(X)= V(Y)= 1 So  V(Z) = V(X+bY)  = V(X)+b2V(Y)  { x and Y are independent} = 1+ b2

Q: Let X be a random variable with mean μ and variance _2. Show that E[(X − b)2], as a function of b,…

A:

Q: If the RVSX1, X2, ..., Xn all have the same variance s and he correlation oxil ficient between each…

A:

Q: Suppose that the response y is generated by y = f(x) + €, where is a zero-mean Gaussian noise with…

A: Given Information: Consider the response y which is generated by:     y=fx+ε Where ε is a zero mean…

Q: If X is a Poisson Variable such that P(X - 2) = 9 %3D P(X= 4 +90 P(X=6). Find the mean, variance and…

A:

Q: Compute the means ur. Hy, and the variances o,

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

Q: Let X, and X, be independent random variables with mean u and variance o?. Suppose that we have two…

A:

Q: A chemical supply company currently has in stock 100 Ib of a certain chemical, which it sells to…

A: Given, X 1 2 3 4 P(X) 0.3 0.5 0.1 0.1

Q: The information associated with the maximum likelihood estimator of a parameter 0 is 4n, where n is…

A: In question, We have given that MLE of theta is 4n, then we'll find the asymptomatic variance of MLE…

Q: If X and Y are independent normal variates possessing a common mean µ such that P(2X + 4Y 1) = 1…

A: Given:

Q: Let X have a mean of 13 and a variance of 1.1. Let Y have a mean of 9.1 and a variance of 0.75. The…

A:

Q: Consider R.V. Y Unif (0, 1) What is the variance of U -4 In(Y)? %D

A: From the given information, Y~Unif0,1. f(y)=11-0      =1, 0<y<1

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.