The solution to this problem is given below-
Let X1,X2,X3,X4 be observations of a random sample of n-4 from the exponential distribution having mean...
Let x1, x2,x3,and x4 be a random sample from population with normal distribution with mean ? and variance ?2 . Find the efficiency of T = 1/7 (X1+3X2+2X3 +X4) relative to x= x/4 , Which is relatively more efficient? Why?
7.Let X1, X2, X3, and X4 be a random sample of observations from a population with mean μ and variance σ2. Consider the following estimator of μ:⊝1 = 0.15 X1 + 0.35 X2 + 0.20 X3 + 0.30 X4. Is this a biased estimator for the mean? What is the variance of the estimator? Can you find a more efficient estimator?
Let X1, X2, X3, and X4 be a random sample of observations from a population with mean μ and variance σ2. Consider the following estimator of μ: 1 = 0.15 X1 + 0.35 X2 + 0.20 X3 + 0.30 X4. Using the linear combination of random variables rule and the fact that X1, ..., X4are independently drawn from the population, calculate the variance of 1? A. 0.55 σ2 B. 0.275 σ2 C. 0.125 σ2 D. 0.20 σ2
Let X1, X2, X3, and X4 be a random sample of observations from a population with mean μ and variance σ2. The observations are independent because they were randomly drawn. Consider the following two point estimators of the population mean μ: 1 = 0.10 X1 + 0.40 X2 + 0.40 X3 + 0.10 X4 and 2 = 0.20 X1 + 0.30 X2 + 0.30 X3 + 0.20 X4 Which of the following statements is true? HINT: Use the definition of...
Let X1, X2, X3, X4 be a random sample from a standard normal population. What is the probability distribution (give the name of the distribution and the value of any parameter(s)) of (a). (X1 - Xbar)^2 + (X2 - Xbar)^2 + (X3 - Xbar)^2 + (X4 - Xbar)^2 (b). ((X1 + X2 + X3 + X4)^2)/4
4 10 pts. Let X1 X2 be a random sample from the exponential distribution with parameter θ What is the mgf of Y = X1 + X2? a) (4 pts.+) Find E(Y-E(X1 + X2] using the mgf. For 2 more points on test 2: How is Y distributed? 4 10 pts. Let X1 X2 be a random sample from the exponential distribution with parameter θ What is the mgf of Y = X1 + X2? a) (4 pts.+) Find E(Y-E(X1...
Let X1, X2, ..., Xn be a random sample from the distribution with probability density function f(x;t) = Botha, 0 < x < 2, t> -4. a. Find the method of moments estimator of t, t . Enter a formula below. Use * for multiplication, / for division and ^ for power. Use m1 for the sample mean X. For example, 7*n^2*m1/6 means 7n27/6. ſ = * Tries 0/10 b. Suppose n=5, and x1=0.36, X2=0.96, X3=1.16, X4=1.36, X5=1.96. Find the...
Let X1, X2, Xn be a random sample from the distribution with probability density function > - 7+tx 7 f(x; t) 0 x 2 2 14+2t a. Find the method of moments estimator of t, t. Enter a formula below. Use * for multiplication, / for division and A for power. Use m1 for the sample mean X. For example, 7*n^2*m1/6 means 7n2X/6. b. Suppose n-5, and x1-0.60, x2 0.95, x3=1.06, x4 1.18, x5-1.52. Find the method of moments estimate...
Let X1, X2, ..., Xn be a random sample of size n from the distribution with probability density function f(x1) = 2 Æ e-dz?, x > 0, 1 > 0. a. Obtain the maximum likelihood estimator of 1 . Enter a formula below. Use * for multiplication, / for divison, ^ for power. Use m1 for the sample mean X, m2 for the second moment and pi for the constant n. That is, m1 = * = *Šxi, m2 =...
Let X1, X2, ... , Xn be a random sample of size n from the exponential distribution whose pdf is f(x; θ) = (1/θ)e^(−x/θ) , 0 < x < ∞, 0 <θ< ∞. Find the MVUE for θ. Let X1, X2, ... , Xn be a random sample of size n from the exponential distribution whose pdf is f(x; θ) = θe^(−θx) , 0 < x < ∞, 0 <θ< ∞. Find the MVUE for θ.