Question: Let X be a random variable having the exponential distribution Let X be a random variable having the exponential distribution With parameter A1 and let

Let X be a random variable having the exponential distribution

Let X be a random variable having the exponential distribution With parameter A1 and let Y be an independent random variable having the exponential distribution with parameter A2. Note that {X} and {Y} are independent samples each of size 1. 1. Derive the likelihood ratio statistic A for testing H0 : A1 = A2 versus H1 : A1 75 A2. 2. For the likelihood ratio test which rejects H0 for small values of A, deduce that the rejection region is of the form {X / Y > c} U {Y/X > c}. 3. What are the null distributions of X / Y and Y/ X ? 4. Explain how you would select the constant 0 given in part (ii) so that the likelihood ratio test has signicance level a

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

For the following questions provide well detailed answers. Let X be a random variable with an exponential distribution, so that the probability density function is given by: fx(x) = de-dx (i)...

Please help with this homework question and explain. Thank you very much. Question: Suppose X is a random variable following the exponential distribution with parameter . (a) Find the moment...

please answer both and show working 1. (25 points) Two fair 6 sided dice are rolled. What is the probability that (a) a ve turns up exactly once? (b) at least one die roll is a ve, given that the two...

6.17. If X is a random variable having an exponential distribution with the parameter 0, use Theorems 4.10 on page 128 and 6.4 to find the moment-generating function of the random variable Y = X...

Could someone help me with the following questions? Consider now the following scenario: let X be a random variable that follows some distribution. Suppose we observe n instances of X, i.e. we have a...

Let X be a random variable with the probability distribution below. Let X be a random variable with the probability distribution below. Find E(X) and E (X" ) and then, using these values, evaluate...

Let X be a random variable with a continuous distribution such that the interquartile range (IQR) is . Prove that the IQR of aX + b is a for all a > 0 and all b. 12. Let X be a random variable with a...

Let X be a random variable with the probability distribution below. Find ?g(X)?, where g(X)=(2X+3)2. Let X be a random variable with the probability distribution below. Find \"900' where g(X) = (2X +...

Let X be a random variable having the binomial distribution with parameters n = 7 and p = 1/4, and let Y be a random variable having the binomial distribution with parameters n = 5 and p = 1/2.Which...

i just need to solve part 1 please Part 1 Consider a network that has four nodes n1, n2, n3 and n4, and six directed arcs of the form a1 = (n1, n2), a2 = (n1, n3), a3 = (n2, n3 ), a4 = (n3), n2), a5...

Should Galaxy have performed an interim step 1 of the goodwill impairment test on September 30, 20X2, instead of only performing a qualitative assessment test? Identify and quote the specific...

List some factors that can affect productivity and some ways that productivity can be improved.

5 5 Multiple Choice 1 . 6 6 7 points Which one of the following statements is correct? Risks and expected return are inversely related. Risk premiums are inversely related to the standard deviation...

1. Buying groceries at the supermarket. 2. Selling a house 3. Getting married out of community of property. 4. Starting a new cellphone contract. 5. Arranging monthly instalments to pay for the car...

18. In the statements below, put a cross for the statement you feel characterizes yourself best when you communicate with others. Its not necessarily the way you know you should communicate, but the...

10. What activities in your life best express the value you want others to associate with you?

7. Also complete the following sentence: This core value is important to me when I ________________________. This is the situation this core value is important to you we are looking for here.