a)Let Y be a random variable whose probability density function and cumulative distributionfunction is given byand,f(y; 0) =QUESTION 4ey-0(1+ey-8)2,F(y; 0) = 1 -11+ey-0-∞ 1.ii) Find the power of the test which rejects Ho if Y > 1.iii) If a test that rejects Ho given Y₁ ≥c is considered. What will be the value of c when the levelof significance of the test is 0.1.

The level of significance is equal to probability of type I error. The power of test is rejecting H0…

Answered: a) Let Y be a random variable whose…

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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2. Let X₁, X2, ..., Xn represent a random sample from a Poisson distribution with probability mass function given below. p(x) = e-11e0 el x! summary sheet on Moodle and state E(X). X 2 (a) Look up the Special Distributions (b) Find the moment estimator of X. (c) Show that the maximum likelihood estimator of X is the same as the moment estimator. x = 0, 1, 2, ... (d) Estimate A from the following observations using the moment/maximum likelihood. estimator. Round your answer to 4 decimal places. Frequency 18 0 1 2 3 4 5 6 7 37 42 30 13 7 2 1
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For a random variable, its hazard function also referred to as the instantaneous failure rate is defined as the instantaneous risk (conditional probabilty) that an event of interest will happen in a narrow span of time duration. For a discrete random variable X, its hazard function is defined by the formula hX(k) =P(X=k+ 1|X > k) =pX(k)1−FX(k). For a Poisson distribution with λ= 4.2, find hX(k) and use R to plot the hazard function.
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a) Let Y be a random variable whose probability density function and cumulative distribution function is given by b) and, f(y;0) = ey-8 (1+ey-8)² F(y; 0) = 1- " 1 1+ey-8, -∞ 1. ii) Find the power of the test which rejects Ho if Y > 1. iii) If a test that rejects Ho given Y₁ ≥c is considered. What will be the value of c when the level of significance of the test is 0.1. The daily salaries (in rands) for an international bank are normally distributed with mean and standard deviation of 14.20 and 3.50, respectively. Suppose that the bank randomly selected fourty (40) tellers and hire them, paying each teller on average of 12.20 per day. Test at 1% level of significance whether the bank can be accused of paying poor salaries or not?
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