Problem No. 2:Suppose Y₁, Y2,,Y₁ is an iid sample from a population distribution with probability distributionfunction[¾e-²₁ y > 0fy (y)0, otherwiseThe unknown population parameter is 0 > 0.a. Show thatis an unbiased estimator of 0.b. Derive the standard error of 6.

Answered: Image /qna-images/answer/669119c2-2cc5-4ee5-8839-08a210ddb160.jpg

Answered: Problem No. 2: Suppose Y₁, Y2₂,,Y, is…

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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Problems 5 and 6 refer to the discrete random variables X and Y whose joint distribution is given in the following table, so P(X = 1 and Y = -1) = 1/4, P(X = 1 and Y = 1) = 0, etc. Problem 5: Compute the marginal distributions of X and Y, and use these to compute E(X), E(Y), Var(X), and V ar(Y). Problem 6: Compute Cov(X, Y) and the correlation ρ for the random variables X and Y. Are X and Y independent? Y= -1 Y =0 Y =1 X =1 1/4 1/8 0 X =2 1/16 1/16 1/8 X =3 1/16 1/16 1/4
9.1) Suppose X1, X2, and X3, denotes a random sample from the exponential distribution with density function shown in the image. a) Which of the above estimators are unbiased for θ? b) Among the unbiased estimators of θ, which has the smallest variance?
Problem 1. Consider the following density function. f(x )=[ (kx) ^ (2/3) * 0 < x < 2 Find the value of k. Find the cumulative distribution function ( CDF) of X Find the inverse of the CDF. Simulate a random sample of 10000 values from the above distribution by using inversetransformation and find the mean and the variance of those values, and write the Rcode.
Question 1A) A discrete random variable X has probability distribution given by X 1 2 3 4 5 P(X=x) 0.2 0.25 0.14 a 0.05 The value of “a” is.. a.0.45 b.0.64 c.0.36 d.0.20 Question 1B The run time for written C-Programmes for Gaussian elimination follows a normal distribution with a mean of 36 minutes and a standard deviation of 11 minutes. For a C-Programme chosen at random, the probability that the run time will be less than 51 minutes is ? a.0.9131 b.0.1586 c.0.0869 d.0.4131
Problem 10 : Independent random variables {U, X, W} have variances V[U] = 1, V[X] = 2, V[W] = 3.Let Y = 2U + 3X + 4W. Find the standard deviation of Y.
If Y is a discrete random variable with possible values of 1, 2, and 4, and the probability mass function is given by P(Y = 1) = 0.2, P(Y = 2) = 0.5, and P(Y = 4) = 0.3, what is the variance of Y?
QUESTION 3 3.1 Consider the discrete random variable (Y) with the following probabilitydistribution: P (y=y)= 0.05( y+1) for y= 0,1,2,3,93.1.1 Express the probability distribution in tabular form 3.1.2 Find the variance of 2Y + 43.2 A marketing manager makes the statement that the long-run probability that acustomer would prefer the deluxe model to the standard model is 30 percent.3.2.1 What is the probability that exactly 3 in a random sample of 10 customers willprefer the deluxe model? 3.2.2 What is the probability that more than 6 in a random sample of 15 customerswill prefer the standard model?
QUESTION 12 Historically, the proportion of people who trade in their old car to a car dealer when purchasing a new car is 48%. Over the previous 6 months, in a sample of 115 new-car buyers, 46 have traded in their old car. To determine (at the 10% level of significance) whether the proportion of new-car buyers that trade in their old car has statistically significantly decreased, what can you conclude concerning the null hypothesis? Reject the null hypothesis Fail to reject the null hypothesis
QUESTION 12 Historically, the proportion of people who trade in their old car to a car dealer when purchasing a new car is 48%. Over the previous 6 months, in a sample of 115 new-car buyers, 46 have traded in their old car. To determine (at the 10% level of significance) whether the proportion of new-car buyers that trade in their old car has statistically significantly decreased, what can you conclude concerning the null hypothesis?
QUESTION 3 TABLE 2 shows the probability distribution of X number of new handphone sold per day at a cellular phone company kiosk. TABLE 2 X 6 7 8 9 10 11 12 13 14 0.03 0.08 0.15 0.20 0.19 0.16 0.10 0.07 0.02 A) Show that the above distribution is a probability distribution of the random variable X. B) Find the probability that the worker at the kiosk to sell at least 10 new handphones per day. C ) Is it possible for the worker at the kiosk to sell more than 14 new handphones? Justify your answer. D )Draw a graph for the probability of distribution of X. E )Calculate the expected number of new handphones to be sold per day. Interpret the result. F )Compute the standard deviation of new handphones to be sold per day.

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Problem No. 2: Suppose Y₁, Y2₂,,Y, is an iid sample from a population distribution with probability distribution function fy (y) (e-,y>0 0, otherwise The unknown population parameter is 0 > 0. a. Show that -1² is an unbiased estimator of 0. b. Derive the standard error of 6.