20) Use the multinomial formula and find the probability for the following data. n=6, X1 =...
2. Multinomial Data: A multinomial experiment with k=3 cells and n-320 produced the data shown in the accompanying table. Do these data provide sufficient evidence to contradict the null hypothesis that p1 0.25, p2-0.25 and p3-0.5? Assume a Type I error rate of 0.05. Cell ni 78 60 182
2. Multinomial Data: A multinomial experiment with k=3 cells and n-320 produced the data shown in the accompanying table. Do these data provide sufficient evidence to contradict the null hypothesis that...
Description for Question 7. A multinomial distribution for three nonnegative counts X1, X2, X3 has joint pdf given by 23 P(X1 = X1, X2 = 22, X3 = x3) (21.3.2.) pi? pºp3", X1 X2 X3 where pi + P2 + P3 1. For genotypes AA, Aa, and aa, the Hardy-Weinberg model puts the respective genotype proportions in the population at (1 - 0)?, 20(1 – 0), and 02, where 0 is the gene frequency of gene type "a" (0 <...
3. [20 marks] Consider the multinomial distribution with 3 categories, where the random variables Xi, X2 and X3 have the joint probability function where x = (zi, 2 2:23), θ = (θί, θ2), n = x1 + 2 2 + x3, θι, θ2 > 0 and 1-0,-26, > 0. (a) [4 marks] Find the maximum likelihood estimator θ of θ. (b) [4 marks] Find that the Fisher information matrix I(0) (c) [4 marks] Show that θ is an MVUE. (d)...
20 marksConsider the multinomial distribution with 3 categories, where the random variables X1,X2 and X have the joint probability function 123 [4 marks] Find the approximate distribution of Y = 2X1-X2, when the sample size n is large.
20 marksConsider the multinomial distribution with 3 categories, where the random variables X1,X2 and X have the joint probability function 123
[4 marks] Find the approximate distribution of Y = 2X1-X2, when the sample size n is large.
3. [20 marks] Consider the multinomial distribution with 3 categories, where the random variables Xi, X2 and X3 have the joint probability function where x = (zi, 2 2:23), θ = (θί, θ2), n = x1 + 2 2 + x3, θι, θ2 > 0 and 1-0,-26, > 0. (a) [4 marks] Find the maximum likelihood estimator θ of θ. (b) [4 marks] Find that the Fisher information matrix I(0) (c) [4 marks] Show that θ is an MVUE. (d)...
3. Suppose (X1, ..., Xk) follows a multinomial distribution with size n and event probability Pi, i = 1, ..., k. (C-1 Xi = n and Li-l pi = 1). (a) Show Xi~ Binom(pi) for i = 1, ..., k. (b) Show X; + X; ~ Binom(pi + pj), for 1 <i, j <k and i # j. (c) Show Cov(Xi, X;) = -npipj. (Hint: V(X; + X;) = V(X;) + V(X;) + 2Cov(Xi, X;)).
For the given data, find ∑x, n, and x̅: x1 = 16, x2 = 21, x3 = 20, x4 = 17, x5 = 18, x6 = 17, x7 = 17, x8 = 11
Let > 0 and let X1, X2, ..., Xn be a random sample from the distribution with the probability density function f(x; 1) = 212x3e-dız?, x > 0. a. Find E(X), where k > -4. Enter a formula below. Use * for multiplication, / for divison, ^ for power, lam for \, Gamma for the function, and pi for the mathematical constant 11. For example, lam^k*Gamma(k/2)/pi means ik r(k/2)/ I. Hint 1: Consider u = 1x2 or u = x2....
Problem 2 (15 marks) Consider a multinomial experiment involving n = 200 students of a large high school. The attendance department recorded the number of students who were absent during the weekdays. The null hypothesis to be tested is: Ho: p1 = .10, p2 = 25, p3 = .30, p4 = 20, p5 = 15. The following data regarding absenteeism have been collected during the last week. Day of the Week Mon. Tues. Wed. Thurs. Fri. Number Absent 16 44...
Problem 8 (15 marks) Consider a multinomial experiment involving n= 300 students of a large high school. The attendance department recorded the number of students who were absent during the weekdays. The null hypothesis to be tested is: Ho: p1 = .15, p2 = 20, p3 = .30, p4 = .25, p5 = .10. The following data regarding absenteeism have been collected during the last week. Day of the Week Number Absent Mon. 48 Tues. 55 Wed. 92 Thurs. 73...