Suppose the random variable, X, follows an exponential distribution with mean 0 (0 ≤0 <∞). Let X₁, X2,..., Xn be a random sample of size n from the population of X.(a) Find the rejection region for a most powerful test of Ho: 0 = 0o versus H₁ : 0 =0 <00.(b) Is the above test uniformly most powerful? Explain your answer with argument.(c) Show (or argue) that the distribution of Σ₁1X₁ = ²nX is x²n (which can beused to find the constant associated with the rejection region of the above test).

In this problem, we are considering a random variable X that follows an exponential distribution…

Answered: Suppose the random variable, X, follows…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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If we let X1, X2,...X10 be a random sample from the distribution N( μ, σ), then what is the value k so that: P( (X-μ)/(σ/√10) < k ) = .05 P( (X-μ)/(S/√10) < k ) = .05 P( k < (X-μ)/(S/√10) ) = .05
Suppose the distribution of some random variable X is modeled as Negative binomial with parameters, p and r, where p is the probability of success and r is the total number of success over the trials. Find the method of moment (MM) estimators for (p,r), in closed algebraic form expressions based on a random sample of size n, X1, X2,...,Xn.
According to IT department of leading financial firm, 50% of emails received by their employees are spam. They are planning to install a software which filters the spam emails. A reputable cybersecurity brand has launched a software which claims to detect 99% of spam emails. However, they have also reported 5% as the chance of detecting a non-spam email as spam. If an email is detected as spam, what is the probability of it in fact being a non-spam email?
Let X1, ..,Xn be a random sample of distribution f(x; 0)=e-(=-0), x>0, 0 elsewhere, where 0 > 0. (a) Find the mle of 0. (b) For testing Họ : 0 = 00 vs H1 : 0 > 00, find the Likelihood Ratio Test (LRT) in terms of the mle found in part (a)
2 (a) Let Y be the random variable that counts the number of sixes which occur when a die is tossed 10 times. What type of random variable is Y? What is P (Y = 3), expected number of sixes,Var(Y )? (b) Let U be the random variable that counts the number of accidents that occur at an intersection in one week. What type of random variable is U? Suppose that, on average, 2 accidents occur per week. Find P(U = 2), E(U), and V ar(U). (c) Let X be the recorded body temperature of a healthy adult in degrees Fahrenheit. What type of rv is X? Estimate its mean and standard deviation, based on your knowledge of body temperatures.
Consider again the random variable with a cumulative distribution function ofF(x) = x^2/25, for 0 ≤ x ≤ 5. (d) What is the probability of x =1? (e) Do you think x is a symmetric random variable? Why or why not? I need answers of sub-parts (d) and (e) only.
You obtain 336 successes in a sample of size n1=391n1=391 from the first population. You obtain 419 successes in a sample of size n2=472n2=472 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.What is the test statistic for this sample
3
Suppose that a medical test has a 85% chance of detecting a disease if the person has it (P(PT|D)=0.85) and a 90% chance of correctly indicating that the disease is absent if the person really does not have the disease (P(NT|Dc=0.90). Suppose that 95% of the population does not have the disease P(Dc)=0.95 What is the probability that a randomly chosen person will test negative P(NT)?
I need help with this question. Can you please go step by step because I am very confused?
Independent random samples, each containing 70 observations, were selected from two populations. The

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