Problem 5. Find jointly sufficient statistic for the continuous uniform distribution on 01,02 (here, and θ2...
a) Show that Σ.1X, and Σηι x? are jointly sufficient statistics for two un known parameters of the normal distribution N(01,02) (based on the data sample X1,..., Xn) in two ways: by factorization theorem and using the property of the exponential family. b) Show that X and s2 are jointly sufficient statistics for the same distribution. c) Give yet another example of a couple of jointly sufficient statistics. Hint: Example 6.7-5 in Hogg et al. Anyway, make sure to include...
Problem 7 a) Show that n 1 Xi and n 1 X? are jointly sufficient statistics for two un- known parameters of the normal distribution N(01, 02) (based on the data sample Xi,..., Xn) in two ways: by factorization theorem and using the property of the exponential family. c) Give yet another example of a couple of jointly sufficient statistics. solution into your homework (not just refer to the aforementi statistic, have you checked that this function is invertible? b)...
with parameters α and β. 2. Yİ,%, , Y, are a random sample from the Gamma distribution (a) Suppose that α 4 is known and β is unknown. Find a complete sufficient statistic for β. Find the MVUE of β. (Hint: What is E(Y)?) (b) Suppose that β 4 is known and α is unknown. Find a complete sufficient statistic for a. with parameters α and β. 2. Yİ,%, , Y, are a random sample from the Gamma distribution (a)...
Verify whether the following belong to the exponential family and find a sufficient statistic for the unknown parameters? - Gamma distribution with α or β or both α and β unknown
6.1.12 Suppose that (x1,..., xn) is a sample from a Geometric(θ) distribution, where θ ∈ [0, 1] is unknown. Determine the likelihood function and a minimal sufficient statistic for this model. (Hint: Use the factorization theorem and maximize the logarithm of the likelihood.)
Problem 8: 5 points] Let Xi,.,.Xn be IID from a Uniform distribution on (-0,0) where 0 0 is an unknown parameter (a) Find a minimal sufficient statistic T. (b) Define Show that T and V are independent.
Question 1 Solve the problem. If a continuous uniform distribution has parameters of u 0 and a 1, then the minimum 3 and the maximum is 3. For this distribution, find P(-1 < x < 0.5). Round your answer to three decimal places. IS 0.289 0.25 0.433 0.577
Let Yı,Y2, ..., Yn be iid from a population following the shifted exponential distribution with scale parameter B = 1. The pdf of the population distribution is given by fy(y\0) = y-0) = e x I(y > 0). The "shift" @ > 0 is the only unknown parameter. (a) Find L(@ly), the likelihood function of 0. (b) Find a sufficient statistic for 0 using the Factorization Theorem. (Hint: O is bounded above by y(1) min{Y1, 42, ..., .., Yn}.) (c)...
Solve the following two parts: (Hint: Use Complete Sufficient Statistic) Suppose X1 , X2, of λ2 and the UMVUE of (-1)(-1) Suppose X1 , X2, and UMVUE of 1/g? a. , Xn are iid Poisson distribution with mean λ. Find the UMVUE b. , Xn are iid Uniform[0, θ]. Assumen 3. Find UMVUE of θ3
2. Assume the random variable y has the continuous uniform distribution defined on the interval a to b, that is, f(y) = 1/6 - a), a sy<b. For this problem let a = 0 and b = 2. (a) Find P(Y < 1). (Hint: Use a picture.) (b) Find u and o2 for the distribution.