5.5.4. Let Y1, Y2, ..., Yn be a random sample from the uniform pdf fy(y; 0) = 1/0, 0 ≤ y ≤ 0. Compare the Cramér-Rao lower bound for fy (y; 0) with the variance of the unbiased estimator ê = "+1 Ymax. Discuss.
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- The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.02EX7.8) Let Y be a random variable having a uniform normal distribution such that Y U(2,5) 2 Find the variance of random variable Y.5.4.6. Let Ymin be the smallest order statistic in a random sample of size n drawn from the uniform pdf, fy(y; 0) = 1/0, 0 ≤ y ≤0. Find an unbiased estimator for 0 based on Ymin.
- 2.5.8) Suppose that Y is a continuous random variable whose pdf is given by f(y) = {K (4y = 2y²), 0 1). (c) Find F(y).2.4. Let Y,, Y2, .., Yn denote a random sample from a uniform distribution with a pdf given by f(y|e) = }0 03. (20%) Let Wi < W2 < W3 < W4 < W5 < W6 be the order statistics of n = observations from f(x) = x/2; 0 < x < 2. 6 independent (a) Find the pdf of W1 and W6Let X1, . . . , Xn be iid from Exp(β). Find the distribution of the sample maximum Y = X(n). Is this an exponential distribution? (This question was rejected this morning. I did double check and there is no missing info with this question.)1. 2. 3. Let Y₁, Y2, Y3, Y4, Y5 be a random sample of size 5 from a standard normal population. Find the moment generating function of the statistic: X = 2Y₁²+ Y₂² + 3Y3² +Y4² +4Y5² Let Y₁, Y₂, Y3, Y4, Y5 and X₁, X₂,..., X, be independent and normally distributed random samples from populations with means ₁ = 2 and ₂ = 8 and variances ₁² = 5 and ₂² = k, respectively. Suppose that P(Ỹ – Ỹ > 10) = 0.02275, find the value of ₂² = k. Suppose that Y₁, Y₂2, ..., Ym and X₁, X2, Xm are independent normally distributed random samples from populations with means μ₁ and μ₂ and variances ₁² and ₂², respectively. Is X - Y a consistent estimator of ₂ - ₁? Justify your answer.. Suppose X ~ N(2,3). What value of x has a z-score of -0.67?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 .3. Let X1,.., X,, be a random sample from f(r, 0) = , 0 0. Let Y = min;{X,}. Find consistent estimators of 20 +4 and 502 + e° based on Y. %3DQ1. Let X; and S be the mean and variance of independent random samples of size ni from populations with mean H; and variance of (i = 1,2), respectively where u, = 20. of = 9, n1 = 36 and u2 = 18, ož = 16, n2 = 49. Find (- a) P(X, > 20.98) b) x such that P(X, 12.8062) d) si such that P(S} > s3) = 0.80 e) P(X1 – X2 > 0.2336) n P(SE/S글 > 0.8368) %3DSEE MORE QUESTIONS
