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hi..please help me to solve these problem.
(15 marks) 3. Xi, X2, Xs, X4 is a...
1(a) Let Xi, X2, the random interval (ay,, b%) around 9, where Y, = max(Xi,X2 ,X),...
1(a) Let Xi, X2, the random interval (ay,, b%) around 9, where Y, = max(Xi,X2 ,X), a and b are constants such that 1 S a <b. Find the confidence level of this interval. Xi, X, want to test H0: θ-ya versus H1: θ> %. Suppose we set our decision rule as reject Ho , X, be a random sample from the Uniform (0, θ) distribution. Consider (b) ,X5 is a random sample from the Bernoulli (0) distribution, 0 <...
3. [20 marks Consider the multinomial distribution with 3 categories, where the random variables Xi, X2 and Xs have the...
3. [20 marks Consider the multinomial distribution with 3 categories, where the random variables Xi, X2 and Xs have the joint probability function (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) 4 marks Find the approximate distribution of Y 2X-X2, when the sample size n is large (e) [4 marks] Assume that X-(253, 234, 513). Find the...
6. Let Xi, X2, .., X6 be a random sample from a distribution with density function...
6. Let Xi, X2, .., X6 be a random sample from a distribution with density function 820-1 for 0 < x 1 where θ > 0 f(x; 6) 0 otherwise The null hypothesis Ho : θ-1 is to be rejected in favor of the alternative Ha : θ 1 if and only if at least 5 of the sample observations are larger than 0.7. What is the significance level of the test
Please let me know how to solve 7.6.5. 6.5. Let Xi, X2,. .. X, be a random sample from a Poisson distribution with p...
Please let me know how to solve 7.6.5.
6.5. Let Xi, X2,. .. X, be a random sample from a Poisson distribution with parameter θ > 0. (a) Find the MVUE of P(X < 1)-(1 +0)c". Hint: Let u(x)-1, where Y = Σ1Xi. 1, zero elsewhere, and find Elu(Xi)|Y = y, xỉ (b) Express the MVUE as a function of the mle of θ. (c) Determine the asymptotic distribution of the mle of θ (d) Obtain the mle of P(X...
Please answer this question using R 20. Let X1, X2, ..., X12 be a random sample...
Please answer this question using R
20. Let X1, X2, ..., X12 be a random sample from a Bernoulli distribution with unknown success probability p. We will test Ho: p = 0.3 versus Ha: p < 0.3, rejecting the null if the number of successes, Y = Dizi Xi, is 0 or 1. (a) Find the probability of a Type I error. (b) If the alternative is true, find an expression for the power, 1 – B, as a function...
Problem 3.1 Suppose that XI, X2,... Xn is a random sample of size n is to...
Problem 3.1 Suppose that XI, X2,... Xn is a random sample of size n is to be taken from a Bermoulli distribution for which the value of the parameter θ is unknown, and the prior distribution of θ is a Beta(α,β) distribution. Represent the mean of this prior distribution as μο=α/(α+p). The posterior distribution of θ is Beta =e+ ΣΧ, β.-β+n-ΣΧ.) a) Show that the mean of the posterior distribution is a weighted average of the form where yn and...
A random sample of size n -8 is drawn from uniform pdf f(x,θ)- , 0-XS θ for the purpose of testing Ho : θ-2 against H, : θ < 2 at α : 0.10 level of significance. Suppose the decision rule is to be...
A random sample of size n -8 is drawn from uniform pdf f(x,θ)- , 0-XS θ for the purpose of testing Ho : θ-2 against H, : θ < 2 at α : 0.10 level of significance. Suppose the decision rule is to be based on Xmax, the largest order statistic. What would be the probability of committing a Type II error when θ 1.7.
A random sample of size n -8 is drawn from uniform pdf f(x,θ)- , 0-XS...
FF1:18 1H20B B 80 ma2500a16-1 ma2500s14 ma2500a15 ma2500s15 ma2500a17 2. Let Xi, X2 , X10 be...
FF1:18 1H20B B 80 ma2500a16-1 ma2500s14 ma2500a15 ma2500s15 ma2500a17 2. Let Xi, X2 , X10 be a random sample of observations from the N(μ, σ*) distribution where μ is unknown and σ2-10. We reject the null hypothesis Ho : μ-5 in lavour of the alternative hypothesis H1 : μ < 5 if sum of the observations is less than or equal to 35 (a) What is the critical region for the test? (b) Compute the size of the test (c)...
2. Let Xi, X2, . Xn be a random sample from a distribution with the probability...
2. Let Xi, X2, . Xn be a random sample from a distribution with the probability density function f(x; θ-829-1, 0 < x < 1,0 < θ < oo. Find the MLE θ
Please note that question 4 should be answered. QUESTION 3 Let Xi, X2, X, be a...
Please note that question 4 should be answered.
QUESTION 3 Let Xi, X2, X, be a random sample from a distribution with probability density function -10(1-xy-i İf 0 < x < l and θ > 0, otherwise. QUESTION 4 Refer to QUESTION 3 above. E(Xi)- 74-1 (a) Find the method of moments estimator of 0 (b) Find the maximum likelihood estimator of 0.
1(a) Let Xi, X2, the random interval (ay,, b%) around 9, where Y, = max(Xi,X2 ,X), a and b are constants such that 1 S a <b. Find the confidence level of this interval. Xi, X, want to test H0: θ-ya versus H1: θ> %. Suppose we set our decision rule as reject Ho , X, be a random sample from the Uniform (0, θ) distribution. Consider (b) ,X5 is a random sample from the Bernoulli (0) distribution, 0 <...
3. [20 marks Consider the multinomial distribution with 3 categories, where the random variables Xi, X2 and Xs have the joint probability function (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) 4 marks Find the approximate distribution of Y 2X-X2, when the sample size n is large (e) [4 marks] Assume that X-(253, 234, 513). Find the...
6. Let Xi, X2, .., X6 be a random sample from a distribution with density function 820-1 for 0 < x 1 where θ > 0 f(x; 6) 0 otherwise The null hypothesis Ho : θ-1 is to be rejected in favor of the alternative Ha : θ 1 if and only if at least 5 of the sample observations are larger than 0.7. What is the significance level of the test
Please let me know how to solve 7.6.5.
6.5. Let Xi, X2,. .. X, be a random sample from a Poisson distribution with parameter θ > 0. (a) Find the MVUE of P(X < 1)-(1 +0)c". Hint: Let u(x)-1, where Y = Σ1Xi. 1, zero elsewhere, and find Elu(Xi)|Y = y, xỉ (b) Express the MVUE as a function of the mle of θ. (c) Determine the asymptotic distribution of the mle of θ (d) Obtain the mle of P(X...
Please answer this question using R
20. Let X1, X2, ..., X12 be a random sample from a Bernoulli distribution with unknown success probability p. We will test Ho: p = 0.3 versus Ha: p < 0.3, rejecting the null if the number of successes, Y = Dizi Xi, is 0 or 1. (a) Find the probability of a Type I error. (b) If the alternative is true, find an expression for the power, 1 – B, as a function...
Problem 3.1 Suppose that XI, X2,... Xn is a random sample of size n is to be taken from a Bermoulli distribution for which the value of the parameter θ is unknown, and the prior distribution of θ is a Beta(α,β) distribution. Represent the mean of this prior distribution as μο=α/(α+p). The posterior distribution of θ is Beta =e+ ΣΧ, β.-β+n-ΣΧ.) a) Show that the mean of the posterior distribution is a weighted average of the form where yn and...
A random sample of size n -8 is drawn from uniform pdf f(x,θ)- , 0-XS θ for the purpose of testing Ho : θ-2 against H, : θ < 2 at α : 0.10 level of significance. Suppose the decision rule is to be based on Xmax, the largest order statistic. What would be the probability of committing a Type II error when θ 1.7.
A random sample of size n -8 is drawn from uniform pdf f(x,θ)- , 0-XS...
FF1:18 1H20B B 80 ma2500a16-1 ma2500s14 ma2500a15 ma2500s15 ma2500a17 2. Let Xi, X2 , X10 be a random sample of observations from the N(μ, σ*) distribution where μ is unknown and σ2-10. We reject the null hypothesis Ho : μ-5 in lavour of the alternative hypothesis H1 : μ < 5 if sum of the observations is less than or equal to 35 (a) What is the critical region for the test? (b) Compute the size of the test (c)...
2. Let Xi, X2, . Xn be a random sample from a distribution with the probability density function f(x; θ-829-1, 0 < x < 1,0 < θ < oo. Find the MLE θ
Please note that question 4 should be answered.
QUESTION 3 Let Xi, X2, X, be a random sample from a distribution with probability density function -10(1-xy-i İf 0 < x < l and θ > 0, otherwise. QUESTION 4 Refer to QUESTION 3 above. E(Xi)- 74-1 (a) Find the method of moments estimator of 0 (b) Find the maximum likelihood estimator of 0.
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