Suppose you have a joint distribution of x and y where • x has population mean lg and population variance o • y has population mean ly and population variance o and the population covariance between them is Ery. The population Pearson correlation is then given by Ery We collect n pairs of data, (xi, Yi), i = 1, .., n. Each pair is an independent draw from this distribution. (a) Suppose we estimate our population covariance with n 1 E(t; – Ha)(yi – Hy). i=1 Is this an unbiased estimator of the population covariance? Show why or why not.

Q: 2. Find a data set of economic/financial time series with one y variable and two independent…

A: Lett’s start with a simple example where the goal is to predict the stock_index_price (y) of a…

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: In two sets of variables x and y with 40 observationş each the following data were observed: Mean x…

A:

Q: and X, be independent normally distributed random variables. X,has a normal distribution with mean 1…

A: Introduction - Z-score  z=x-μσwhere , μ=population mean x=score σ=standard deviation +

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: The variables X and Y with zero means and standard deviations of and O₂ are normally correlated with…

A:

Q: If the random variable X and Y have the joint probability distribution f(x, y) = x+y, 0<x< 1,0 <y<1…

A:

Q: Example 9-32. Show that the mean value of positive square root of a y (u) variate is T(u +;)/T(u).…

A:

Q: The number of accidents in a city follows a Poisson process with a mean of 2 per day and the number…

A:

Q: 4. X and Y are two random variables with variances ožand of respectively and r is the coefficient of…

A: Introduction :  Definition : correlation coefficient: Let X and Y are two quantitative variables.…

Q: Suppose that { Y,} is Moving average process with Y, = 0.25(e, + e,-1+e-2+ej_3) %3D where {e,} is…

A: Find Mean, variance, auto covariance function and auto correlation function

Q: Suppose you are going to invest equal amounts in three stocks. The annual return from each stock is…

A: Hi! Thank you for the question, As per the honour code, we are allowed to answer three sub-parts at…

Q: Suppose Y₁, Y2,, Yn is an iid sample from a gamma population distribution with shape parameter a = 2…

A:

Q: Suppose the variance of the difference of two random variables X and Y is zero. Then, show that X =…

A: A random variable is a function that associates a real number with each element in the sample space.…

Q: Let X is continuous uniform (1,7) and Y is exponential with mean 2. If the correlation coefficient…

A:

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: Let X and Y be independent random variables with means x,y and variances o, oy. Find an expression…

A:

Q: .3 Arandom variable X has a variance of 9 and a statistically independent random variable Y has a…

A: Solution

Q: Two random variables X and Y have meáns-1 and 2 respectively and variances 4 and 1 respectively.…

A: Given,x¯=1 , y¯=2σx=2 , σy=1and r(x,y)=0.4

Q: Suppose X,,X,...,X, is a random samples from normal distribution with mean, uand variance, ΣΧ 1 and…

A: Sum of chi square is always chi square

Q: The Central Limit Theorem states: Let X1,... , X,, be a random sample with E[X,] = H and Var(X) =…

A:

Q: 10. Two variables x and y have zero means, the same variance o and zero correlation, show that x cos…

A:

Q: Let the random variables Y, Y2, ... , Ys be normally distributed with mean 10 and variance 4. Find a…

A: Given that Yi, i = 12,3,4,5 follows N(mean = 10, variance = 4)

Q: - Let y1, Y2, ..., Yn be a random sample of n observations from an exponential distribution with…

A: Given information: Let Y1, Y2, …, Yn is a random sample of size n taken from a exponential…

Q: Two Gaussian random variables X and Y have variances of = 9 and oy= 4, %3D respectively and…

A:

Q: Suppose X,,X,,...,X, is a random samples from normal distribution with mean, µand variance, ΣΧ 1 and…

A:

Q: 5. In a study with one sample drawn from a population, sampled individuals are observed on the…

A: Repeated-measures study: The study in which the subjects are observed two or more times on the…

Q: Suppose W = (aX + 3Y) 2 where Y, X are two random variables with zero mean and variances 20x = 4,…

A: As, X~N(0,4) and Y~N(0,16) E[x] = 0 Var[x] = 4 E(x)2 - [E(x)]2 = 4 E(x)2 - 0 = 4 E(x)2 = 4 Now, E[y]…

Q: Suppose that the Cumulative distribution function (CDF) of the random variable X with parameter e >…

A:

Q: Let X1, X2,.. , X, be a random sample from a normal distribution with mean 0 and variance 4, let Y1,…

A:

Q: company has found that its profits Y are related to its sales X by the formula   Y = 0.2X + 100. If…

A: The profits of y is, Y=0.2X+100. The next year’s sales have a Normal distribution with a mean of…

Q: A random sample of n 20 winter days in Denver gave a sample mean pollution lindex x, 43. Previous…

A: Given information-

Q: Two Gaussian random variables X and Y have variances o =9 and o = 4 respectively, It is known that a…

A:

Q: a) If a distribution is skewed, it's better to give the median and IQR instead of the mean and…

A: HERE AS PER POLICY I SHOULD HAVE  TO CALCULATE 3 SUB PART EVEN THOUGH I HAVE CALCULATED 4 here use…

Q: Suppose we observe two independent random samples X1,... , X, with each X, ~ N (141, 0²) and…

A: We want to find 95% CI for ratio of population variances

Q: Let X₁ a random variable with expected value (mean) E(X₁)= 17 and variance V(X₁) = 12. Let X₂…

A: It is given that, E(X1)= 17 E(X2)= 22 Var(X1)= 12 Var(X2)= 16 Cov(X1,X2)= 9 Var(Y)= Var( 9X1+10X2 )…

Q: Let X1, X2, ..., X, be a random sample from the population N(µz,0²) and Y1, Y2,...,Ym a random…

A: Given information: Given that X1, X2, … , Xn be a random sample from the population N(µx, σ2) and…

Q: 21 - The average weekly income of 50 students randomly selected from a class is 250 TL with a…

A: The variable with the greatest variance will be the one having the largest variation Here the sample…

Q: Suppose we observe two independent random samples X1,..., Xn, with each X; ~ N(µ1,o²) and Y1,...,…

A: The given values are x¯=10.1,y¯=7.1,sX2=5.5,sY2=6.4,n1=13,n2=19.

Q: Suppose X,,X2,..,X, is a random samples from normal distribution with mean, µand variance, ΣΧ 1 and…

A:

Q: Suppose that the random variable X has a Gamma Distribution with parameters a = 2 2 and ß = where .1…

A: Given information:  A random variable X has a Gamma distribution with parameters α and β. Therefore,…

Q: There are two random variables X and Y, and their correlation coefficient pX,Y = 0.7. Now, we have…

A:

Q: Find a number b such that P [(S1^2/S2^2)<=b]=0.95 enter such a b to three decimal places b= 2.…

A: b=3.10 and a=0.35 (Using F distribution table).

Q: from the split data. c

A: Given Information: Dependent variable: Graduation rate Independent variables: (i) % of classes under…

Q: The sales manager of a large company selected a random sample of n = 10 salespeople and determined…

A: a. The sample contains the years of experience in sales, x and the annual sales (thousand dollars),…

Q: Let X be a random variable and Y = aX + b with a ̸= 0. Show that the correlation between X and Y is…

A: Given data: Let X be a random variable and Y = aX + b with a ≠ 0. To show: Show that the correlation…