Problem 5. Suppose that the random variables X₁,, X, form a random sample of size n from acontinuous distribution with CDF F. Let Ymin = min{X1, , Xn} and Ymax = max {X1,,Xn}....Compute E(Ymin) and E(Ymax).

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Answered: Problem 5. Suppose that the random…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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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
chapter 8 question 11 suppose a simple random sample size of size n= 15 is obtained from a population with u=61 and q=14. The population must be normally distributed the sampling distribution of xbar is normal with ux= 61 and q = 14 over the square root of 15. B. P(xbar less than 64.6 assuming the normal model. assuming the normal model, p(x greater than or equal to 63.2
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.
Find the cumulative distribution function of the random variable X representing the number of defectives in Problem #5. Then using F(x), find (a) P(X = 1); (b) P(0 < X ≤ 2).
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?
Questions 2-4 are based on the following scenario. Mr. Lange draws two independent random samples from normally-distributed popula- tions with unknown population means and unknown population vari- ances. The first sample is found to have x = 78, s21 = 25, and n = 10; while the second sample is found to have y = 74, s2 = 9, and n = 16. 2. Mr. Lange wishes to know if there is enough evidence to conclude that the population variances differ. Answer the following questions. (a) State the competing theories of this test. (b) Are the requirements for the Equal Variances F Test met? If not, explain why. (c) Compute the F statistic. Round your answer to three decimal places. (d) What distribution does the F statistic have? (e) Compute α0 as discussed in class. What conclusion can you draw? 3. Mr. Lange wishes to use Welch’s T Test to determine whether there is enough evidence to conclude the population means differ. Answer the following questions. (a) State the…
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 2A 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 P(1 ≤ X ≤ 3) is a.0.25 b.0.41 c.0.34 d.0.59 Question 2B 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 Variance of X … Var(X) is a.1.5739 b.6.6660 c.2.810 d.9.470

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Problem 5. Suppose that the random variables X₁,, X, form a random sample of size n from a continuous distribution with CDF F. Let Ymin = min{X1, Compute E(Ymin) and E(Ymax). Xn} and Ymax = max {X1,,Xn}.