Let X1 be the sample mean of a random sample of size n from a Normal(µ, o7) population and X2 be the sample mcan of a random sample of the same size n from a Normal(4, o) population and the two samples are independent. Note that the two samples have the same population Imean ți but o o. Let i = wX1 +(1 – w)X2,0

Calculate the Average and the variance

For a random sample X1, X2, ..., X, following an Exponential(rate = 1/μ) distribution, we have seen that the large sample distribution of the sample mean X follows a Normal distribution with mean parameter µ and the variance parameter μ²/n. Suppose that we have a sample of size n = 25 from an exponential population with mean μ and we want to test n Hoμ = 2 v/s Hд μ # 2. Use the large sample distribution of ☑ to compute an approximate p-value for the test if we observe x = 2.6 and state the conclusion of your test at the 5% level of significance.

k = Question 5 Suppose the random variables X and Y have a pdf given by f (x, y) = x+y on 0 Y). prob = b. Find F (,글): ans = Question 6 ch 30 Hisense