2.suppose that x1,x2,...,xn be ar.s of size n from exponential dist. with parameter 0, find the MVBE for the parameter 0 and the variance of its?

6. Show that 1 s2 E1(Xi – x)² is unbiased estimator of the population variance o? i=1 п-1

Consider the one-way analysis of variance model Xij = µ + a; + Eij, i= 1,.., m, j= 1,..., ni, where ɛij ~ N(0,0²) are independent. Let n= n1 + · ·+ nm, ... ni 1 ni 1 X;. >Xii for i = 1,..., m, and X. = - ΣΣΧ. ni j=1 i=1 j=1 (a) Show that SS(TO) = SS(T) + SS(E), where SS(TO) = E E i=12j=1 (Xij – X..)², m m ni SS(T) Σι (X.-Χ.) and SS(E) -ΣΣ (Χ- X.) . i=1 i=1 j=1

3.3.24. Let X1, X2 be two independent random variables having gamma distribu- tions with parameters a₁ = 3, B₁ = 3 and a2 = 5, B2 = 1, respectively. (a) Find the mgf of Y = 2X₁ +6X2. (b) What is the distribution of Y?

4, 12. How Call v. 13. Suppose that two raters (Rater A and Rater B) each assign pirysica attractiveness scO = not at all attractive to 10 = extremely attractive) to a set of seven facial photogranhe 21 %3D Pearson's r can be used as an index of interrater reliability or agreement on quantitative ratings. A correlation of +1 would indicate perfect rank-order agreement between rate while an r of 0 would indicate no agreement about judgments of relative attractiveness An r of .8 to .9 is considered desirable when reliability is assessed. For this example, Rater A's score is the X variable and Rater B's score is the Y variable. The ratings are as followe F follows: Photo Rater A Rater B 1 3. 5. 8. 6. 7. 8. 6. 4. 6. 10 6. 7. 5. 4. a. Compute the Pearson correlation between the Rater A and Rater B attractiveness ratings. What is the obtained r value? b. Is your obtained r statistically significant (using a =.05, two tailed)? Are the Rater A and Rater B scores "reliable"? Is there good or…

9. Let 7 = 1.135013 be the sample mean of an iid sample r1,..., T50 from a gamma population Gamma(1, 3). Here ß > 0 is the unknown paramcter of interest. Construct an approximate 95%-CI for ß.

Suppose that y, is an independent response variable (i = 1.....n) with mean, such that g(i) = n₁ = X₁B, where g(.) is a link function, X, is a vector of covariates and 3 is a px 1 vector of coefficients. Let the variance of y; be Var (Y) = V(i), where V(.) is a known function and is a scale parameter. Given: Zi= g'(pi) (Yi - Pi) + Ni w₁ = [V (pi) (g'(pi))²]-¹ 8 where g'(μ) = 9(μ) (a) Show that E(Z₁) = X₂B (b) Show that Var (Z₁) = w¹o. (c) Estimate 3 by minimizing Σ, wi( E(Z₁))² with respect to 3. After you found 8, find the Var(8) and E(3). What do you conclude?

Below are bivariate data O each of twelve countries. For each of the countries, both x, the number of births per one thousand people in the population, and y, the female life expectancy (in years), are given. Also shown are the scatter plot for the data and the least-squares regression line. The equation for this line is ing birthrate and life expectancy information for y = 81.87 – 0.46x. Birthrate, x (number of births per 1000 pop.) Female life expectancy, y (in years) 85- 35.7 67.7 80- 41.5 63.9 75 31.9 63.3 19.9 73.0 70 50.5 60.4 65. 24.4 72.7 60- 50.1 63.2 55 13.8 72.5 50 50.3 54.6 45.6 57.9 15.9 76.2 Figure 1 26.6 71.9 Send data to Excel