If X1,X2,...,Xn constitute a random sample of size n from a gamma population with α =2, use the method of maximum likelihood to find a formula for estimating β.
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If X1,X2,...,Xn constitute a random
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- PLEASE HELP ME ASAPPlease help me for Question 1A large population (consisting of measurements of diameters of ball bearings) has mean u and standard deviation o, neither of which is perfectly known. A random sample of size n = 25 observations will be taken, namely the diameters U1, U2, ·.., U25 will be observed. In other words, U1, U2, · .., U25 are independent and identically distributed random variables with u = E(U1) and Var(U1) = o². No further knowledge about the shape of the distribution is known. Define, 25 1 X 25 Ui 25 i=D1 (i) If someone says E(X 25) = 13, what information does he give you about u, if any? (ii) If someone says o = 5, what is Var(X25)? • (iii) What is the chance, approximately, that a sample of size n = 25 will have its mean, X25, smaller than the population mean u? In other words, find an approximation of P(X 25 < u). [Hint: see if the value of o is relevant or not to answer the question.] (iv) In part (iii) while approximating what theorem did you use, if any? • (v) What is the chance, approximately, that…
- b) Let X1, X2, .,X, be a random sample from a normal distribution with known .... mean u. Using a distribution of U = E, , Mr Mbalula showed that a 100(1 – a)% two sided confidence interval for o? is give by E(X – 4)² £=(X; – µ) | xả. Prove whether or not Mr Mbalula is correct.A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 114, and the sample standard deviation, s, is found to be 10. (a) Construct a 96% confidence interval about u if the sample size, n, is (b) Construct a 96% confidence interval about u if the sample size, n, is (c) Construct a 99% confidence interval about u if the sample size, n, is (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? Click the icon to view the table of areas under the t-distribution. (a) Construct a 96% confidence interval about u if the sample size, n, is 19. Lower bound:; Upper bound: (Use ascending order. Round to one decimal place as needed.) CREEPWe are wondering if the proportions of voters who rejected the proposal to institute astate lottery vary by sex. Random samples from each sex are gathered and the following samplestatistics computed. For males (sample1): •proportion (p1) =0.35 •Sample size (n1) =178 For females (sample2): •Proportion (p2) =0.25 •Sample size (n2) =212 Test the research question atα=0.05 (two-tailed) with the five-step processes and concludeyour decisions. 1. Evaluate assumptions if we can use at-test and summarize parameters and statistics. 2. State the null hypothesis (i.e.,H0) and the working hypothesis (i.e.,H1). 3. Establish the critical region fort-distributions atα=0.05with a two-tailed test. 4. Compute the test statistics (i.e.,tobtained) and the corresponding probability (i.e.,p-value). 5. Make a decision and interpret test results.
- For a two-tailed independent samples t test with a = 0.05 and N1 = 30 & N2 = 32, the critical value(s) should be t?Let X1, X2, *. Xn be a random sample of size n from norm population with mean and unknown a. Let X and s be the sample mean and sample standard deviation. Then for any 01.ln a simple model Y = Bo + B1X +u, X is endogenous, and Z is an instrumental variable that satisfy the relevance and exogeneity conditions. Show that the two stage least squares (TSLS) estimator is consistent. 2.In above model, what is the asymptotic distribution of TSLS? How can we do a). hypothesis testing of Bi and b). construct confidence interval for B,?11. Consider a random sample Y₁, Y2, ..., Yn from a normal population Y~N(μ, o²) where the population variance and mean are unknown. We want to construct a Σ(X-X)² Show 100(1 a)% confidence interval for the population variance if g² whether or not is a pivotal quantity and construct a 100(1-a) confidence interval.(Mathematical Statistics) Let X1,X2,...,X5 be a random sample of the Gamma distribution with parameters a = and ß = 0, e > 0. Determine the 95% confidence interval for the parameter e based on the statistic E(i=1 - 5) Xi. 2Two independent samples are selected at random from two normal populations, where the unknown population variances are assumed to be equal. The sample statistics are as follows: n₁=20,x=40,s=18,n₂=10x₂=34 and $₂=16. Assume that a two-tailed hypothesis test is conducted at α = .05, what is the upper critical value? a. t = 2.0484 b. z = 1.96 c. t = 1.7011 d. z = 1.65 e. t = 1.562SEE MORE QUESTIONS
