If X1 is the mean of a random sample of size n from a normal population with the mean u and the variance o, X2 is the mean of a random sample of size n from a normal population with the mean µ and the variance o, and the the estimator w.X + (1 w). X2 is the unbiased estimator. Is this estimator consistent?

Q: 1. Suppose that X1 and X2 are random variables with zero mean and unit variance. If the correlation…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: We have talked about the fact that the sample mean estimator X = X; is an unbiased estimator of the…

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Q: 4. Suppose the variance of X is 2.0091. Which of the following is(are) TRUE? L In the long run, the…

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Q: Suppose that a sample of size 4 is taken from a population with mean µ and variance 2 . Let x, be…

A: X4 and X9 are two samples drawn from a population with mean μ and variance σ2. We can say that X4…

Q: If X is normally distributed with a mean of 6 and a variance of 25, P(|X-6|<5) P(|X-6|<10)…

A: As per guideline expert have to answer first three subparts only dear student please upload other…

Q: Consider the following regression model: Y₁ =B₁ + B₂X₂1+ B3X31+ B₂X41 +24₁ Using the model above…

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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: Let X1. X2.Xp are independent random samples taken from population with mean and variance of u and…

A: Note: Hi there! Thank you for posting the questions. As there are several independent questions,…

Q: a hypothesis test produces a t statistic of t=2.3. if the researcher is using a two tailed test with…

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Q: Let X1, X2, ..., Xn denote a random sample from a population with mean u and standard deviation o.…

A: 1) The expected value and variance of  (x-bar)-square  is obtained as follows:

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: Suppose you fit a simple Poisson model such that In A = XB where B= 1.7. What would the variance be…

A: question:

Q: 1. Suppose that X1 and X2 are random variables with zero mean and unit variance. If the correlation…

A: Hi, thanks for the question. Since there are multiple questions posted in the question, we will…

Q: 7.9 Let X1,...,Xn be iid with pdf f(x|e) : * 0 0. Estimate 0 using both the method of moments and…

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Q: I. If X1, X2, ...,Xn constitute a random sample from a population with the mean µ, what condition…

A: An estimator c is said to be unbiased estimator of µ is E(c) = µ.

Q: The farmers' association of the Amatole region in the Eastern Cape wants to report on the average…

A: Given that Y1, Y2, Y3, Y4 is a random sample of farms, which is normally distributed with mean μ and…

Q: Let X ~N(0,E²). Find the CRLB for variances of the unbiased estimator of T(0) = e². %3D

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Q: Suppose that xi and x2 are random samples of observations from a population with mean m and variance…

A: Given Information: Mean of x1 and x2=mvariance of x1 and x2=s2No. of point estimators=03…

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&lt;x)=12%=0.12x=?

Q: Consider the following model: Y1 = a +y+E1 Y2 = a+ 8+ €2 Y3 = 6-Y+€3 Y4 = a - y+28 + €4 where a, y…

A: We have given the models  Where alpha beta and delta are unknown constant and ei follows…

Q: If X, and X2 are the means of independent random sample of sizes n and n2 from a normal population…

A: Minimum varience of z=w*x1bar+(1-w)*x2bar is =sigma^2/(n-1+n2)

Q: If X, and X2 are the means of independent random sample of sizes n and n2 from a normal population…

A: Minimum varience of the estimator w*x1bar+(1-w)*x2bar is sigma^2/(n-1+n2) And value of w at which…

Q: f we set the criterion probability (alpha) at .05, and we are conducting a one-tailed test where we…

A: Significance level α=0.05 We are conducting a one tailed test, where we are testing attitude scores…

Q: If X is a Gaussian random variable with mean zero and variance o, find the pdf of Y = \XI.

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Q: If X1 is the mean of a random sample of size n from a normal population with the mean u and the…

A: Here,      X1  is mean of r.s  of size n  from Nμ, σ12  &amp;  X2  is mean of r.s of size   n…

Q: ne sample has a variance of s2 = 10 and the second sample has a variance of s2 = 20.   If the pooled…

A: Given that  One sample has variance of  s2 = 10 Second sample has the variance of s2 = 20.    We…

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: If x, x2 ... Xn is a random sample from N (µ, o²) popula- tion, find sfficient estimator for µ and…

A: ANSWER: For the given data,

Q: Let X1, ..., Xn be a sample from an exponential population with parameter λ. (a) Find the maximum…

A: (a) The probability distribution function for the exponential distribution with parameter λ is given…

Q: To test the hypothesis Ho: u= 25 against H1: u= 28 a sample of four units is selected from a…

A: Given: H0: mu =25 H1 : mu =28 Sample size = 4 population variance = 36 population standard deviation…

Q: 4. Let X~N(0, E²). Find the CRLB for variances of the unbiased estimator of T(0)= e.

A: Question 4  Given  X~N(0,θ2) , variance=θ2, find CRLB for variance

Q: Example 11. Find the mean values of two random variables x and y and the correlation pefficient…

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Q: Suppose you fit a simple Poisson model such that In A = XB where B = 1.9. What would the variance be…

A: Given data

Q: A population has a u=50 and o=10. If these scores are transformed into z- Scores, the population of…

A: Given that mean =  E(X) = 50 and SD(X) = 10, then  Var(X) = 102 = 100

Q: 2. Suppose that in a certain chemical process the reaction time y (hour) is related to the…

A: We have to answer questions based on simple linear regression method.

Q: Let X-N(0,02). Find the CRLB for variances of the unbiased estimator of T(0)= e?.

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Q: 2. Suppose Xi, X2,.. Xn are sample values independently drawn from population with mean u and…

A: Given, X1,X2,X3,.....,Xn  are IID random sample

Q: A sample is selected from a population with population mean = 50 After a treatment is administered…

A: Provided information, n= 36 ,= 55 , S2 = 64 S= 8 ,  =50 Step 1 : We want to test the following null…

Q: 6. Show that 1 s2 = TE2-1(Xi – x)² is unbiased estimator of the population variance o?

A: Show that S^2 is unbiased estimator of population variance

Q: Let s be the sample variance of a random sample of size n1 from a Normal(41,o²) population and s be…

A: Let us understand the distribution of sample variance as follows: Let Xi (i=1,2,......,n) be a…

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…

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Q: Suppose that index model for Stocks A and B is estimated from excess returns with the following…

A: Residual variance is also called as unexplained variance or error variance. It is the variance of…

Q: 1) Suppose the following model y; = B1 + u; Where u; is assumed to be normally distributed with mean…

A: In simple linear regression the model contains a random dependent variable y and a hypothesized…

Q: A random sample of n1 = 11 winter days in Denver gave a sample mean pollution index x1 = 43.…

A: a) The level of significance is 0.01.

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 X1 and X2 constitute a random sample of size n = 2from an exponential population, find the…

A: If X1 and X2 are two estimator of parameter ө, then efficiency of X1 with respect to X2 is obtain as…

Q: If X1, X2, and X3 constitute a random sample of sizen = 3 from a normal population with the mean μ…

A: Given, X1, X2, X3~N (µ, σ2) i.e. E(Xi)=µ and Var (Xi)=σ2 Let,

Q: d. Of all possible estimators of a and ß that are linear in the Y; and unbiased, the least squares…

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Q: Consider two exponentially distributed random variables X and Y, both having a mean of 0.50. Let Z =…

A: Given: X and Y are exponentially distributed with mean 0.5 Z = X+Y Var(Z) = 0 r = ?

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.