Let X₁, Xn be a random sample of size n from the U(0, 0) distribution, where > 0 is an unknown parameter. Recall that the pdf fof the U(0, 0) distribution is of the form [0-¹ f(x) = { {0¹ if 0
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- Let the random variable X be defined on the support set (1,2) with pdf fX(x) = (4/15)x3, Find the variance of X.Let x1, .. , Xn be a random sample with pdf is given by f(x) = {0(1+x)-(1+0), 0, x> 0 otherwise. Find the MLE .Let Y, represent the th normal population with unknown mean 4, and unknown variance of for i=1,2. Consider independent random samples, Y₁, Y2. Yin, of size n₁, from the ith population with sample mean Y, and sample variance S² = ₁₁-1(Y₁-₁². j=1 (g) For non-zero constants a's, what is the distribution of U₂ = a₁Y₁-a₂Y₂? State all the relevant parameters of the distribution. (h) Find the standard error of U₂ in part (g), assuming that of = 0² = 0². (i) Discuss how the distribution of Y₁ - ₂ can be used to test the equality of the two population means, #₁ and μ2, when o² = 0 = 0² is known. (j) Define appropriate rejection regions, in terms of Y₁ - Y2, for testing Ho: #₁ = 2 against a two-sided alternative hypothesis at the a level of significance.
- Develop a random variate generator for a random variable X with the pdf if 0Let X be a continuous random variable with pdfLet x1,x2,..x n be an jid sample with pdf f(x|0)=0X (® -1) OSxs1,0>0 Find the MLE of 0.Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable-X for the right tire and Y for the left tire, with joint pdf f(x, y) ĮK(x? + y?) 21 25). (Round your answer to three decimal places.) P(Y > 25) = (c) If the pressure in the right tire is found to be 22 psi, what is the expected pressure in the left tire, and what is the standard deviation of pressure in this tire? (It is known that K = Round your answers to two decimal 410,600 places.) expected pressure psi standard deviation psiQ3) Let X1,X2,. X, be a random sample from the truncated exponential distribution with pdf: f(x,0) = Please else (a) Derive the method of moment estimator of 0; (b) Derive the MLE of 0. (c) Are the MOME and the MLE unbiased estimators for 0? (d) Compare the MSE of the MOME and the MLE for 0. Which one is a better estimator for 0Let X be a random variable with uniform distribution on the interval [-2,2]. Let Y be defined as Y = X5. Calculate the pdf of Y.SEE MORE QUESTIONS