5. Let X ∼ Beta(α, β). Recall that we showed E(X) = α in class. Find the second moment of x and the variance of x
5. Let X ∼ Beta(α, β). Recall that we showed E(X) = α in class. Find...
Suppose X ~ Beta(a, β) with the constants α,β > 0, Define Y- 1- X. Find the pdf of Y.
Recall that if X has a beta(a, B) distribution, then the probability density function (pdf) of X is where α > 0 and β > 0. In this problem, we are going to consider the beta subfamily where α-β θ. Let X1, X2, , Xn denote an iid sample from a beta(8,9) distribution. (b) The two-dimensional statistic nm 27 is also a sufficient statistic for θ. What must be true about the conditional distribution (c) Show that T* (X) is...
Please answer A.6.6.: The previous two questions mentioned above are included below: A.6.6. We mentioned in class that the Gamma(, 2) distribution when k is a positive integer is called the Chi-square distribution with k degrees of freedom. From the previous two problems, find the mean, variance, and MGF of the Chi-square distribution with k degrees of freedom. A.6.5. In class we showed that if X ~ Gamma(α, β) then E (X) = aß and uar(X) = αβ2 by using...
i need the answer to 6-c 5. A professor has a large class. The proportion of students who miss an assignment is a beta distribution with parameters with α and β 2. (a) Determine the probability that at least 70% of the students will miss an assignment. 6. Using the distribution given in problem 5 (b) What is the expected proportion of missed assignments? (c) What is the variance of this distribution? 5. A professor has a large class. The...
3. Suppose X ~ Beta(a, β) with the constants α, β > 0, Define Y- 1-X. Find the pdf of Y
Let Y1,…,Yn~iid Gamma(5,β). Recall that Γ(5) = 4! a) Find the MLE for β. b) Is your answer to a) the MVUE? Use two methods to verify that it is unbiased.
(10) For a random sample of size n from a Beta(α, β) density, find a consistent estimator of β . Why is this estimator consistent? (10) For a random sample of size n from a Beta(α, β) density, find a consistent estimator of β . Why is this estimator consistent?
7.60 Let Xi, of 1/β. , xn be iid gamma(α, β) with α known. Find the best unbiased estimator
b. Suppose ~ Γ(α, β), with α > 0, β > 0 and let Y-eu. Find the probability density function of Y Find EY and var(Y)
The general solution to the second-order differential equation d2ydt2−4dydt+7y=0d2ydt2−4dydt+7y=0 is in the form y(x)=eαx(c1cosβx+c2sinβx).y(x)=eαx(c1cosβx+c2sinβx). Find the values of αα and β,β, where β>0.β>0.Answer: α=α= and β=β=