Only need answer for question d) 1. Let X₁, X2, and X3 represent the times necessary to perform three successive repairs tasks at acertain service facility. Suppose they are independent, normal random variables with expectedvalues µ‚ µ², and µ and variances σ²,02, and o3, respectivelya) If μ₁ = μ₂ = μ₂ = 60 and σ² = 0² = 03 =15, calculate P(X₁ + X₂ + X3 ≤ 200).b) Using the u's and o's given in part (a), calculate P(58 ≤ X ≤ 62), whereX₁ + X₂ + X3123c) Using the u's and o's given in part (a), calculate P(-10 ≤X₁ – 0.5X₂ – 0.5X3 ≤5).d) If μ = 40, μ₂ = 50, µ = 60, o² =10, o² = 12, and o² =14, calculate P(X₁ + X₂ − 2X3 ≥ 0).X=

d) Let Y=X1+X2-2X3 Consider, E(Y)=E(X1+X2-2X3) =EX1+EX2-2EX3 =μ1+μ2-2μ3 =40+50-2*60…

Answered: Let X₁, X2, and X3 represent the times…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Let X1 and X2 constitute a random sample from a nor-mal population with σ2 = 1. If the null hypothesis μ = μ0 is to be rejected in favor of the alternative hypothesis μ = μ1 > μ0 when x > μ0 + 1, what is the size of the criti-cal region?
Let x and y be random variable such that the mean and variance of X are 2 and 4. respectively, while the mean and variance of y are 6 and k, respectively. A sample of size 4 is taken from the x-distribution and a sample of size 9 is taken from the y-distribution .If p[(x-y)>8]=0.0228,then what is the value of the constant k?
Suppose that three random variables X1, X2, X3 form a random sample from the uniform distribution on interval [0, 1]. Determine the value of E[(X1-2X2+X3)2]
Suppose that a random sample from a normal popula-tion with the known variance σ2 is to be used to test the null hypothesis μ = μ0 against the alternative hypothe-sis μ = μ1, where μ1 > μ0, and that the probabilities of type I and type II errors are to have the preassigned val-ues α and β. Show that the required size of the sample is given by n = σ2(zα + zβ)2(μ1 − μ0)2
Consider a random sample X1,...,Xn,... ∼ iid Beta(θ,1) for n > 2. Prove that the MLE and UMVUE are both consistent estimators for θ
Suppose that the random variable X follows a beta distribution with alpha=1 and beta=3, Beta(1,3) Find p(x>1/3) In R simulate n = 1000 from Beta(1,3) p(x>1/3) and verify the probability is close to the theoretical.
Consider X₁, X₂, . . . , Xn to be independent random variables from a Normal(μ,σ ² ) where both parameters are unknown.
Show that for a random variable X with mean μ and variance σ^2, the standardized random variable Z corresponding to X has mean 0 and variance equals 1 by using the properties of expectation and variance.
For an initial investment of 100, an investment yields returns of Xi at the end of period i for i = 1,2, where X1 and X2 are independent normal random variables with mean 60 and variance 25. What is the probability the rate of return of this investment is greater than 10 percent?
Suppose X, Y, Z are iid observations from a Poisson distribution with parameter λ, which is unknown. Consider the 3 estimators T1 = X + Y − Z, T2 = 2X + Y + Z 4 , T3 = 3X + Y + Z 5 . (a) Which among the above estimators are unbiased? (b) Among the class of unbiased estimators, which has the minimum variance?
7 Let X1,...Xn be iid Normal( θ+ c, σ^2), where c and σ ^2 are known constants (i.e., E(Xi) = θ + c). Find a sufficient statistic forθ then obtain the minimum-variance unbiased estimator for θ.
Let p1 and p2 be the respective proportions of women with iron-deficiency anemia in each of two developing countries. A random sample of 1900 women from the first country yielded 513 women with iron-deficiency anemia, and an independently chosen, random sample of 1700 women from the second country yielded 515 women with iron-deficiency anemia. Can we conclude, at the 0.10 level of significance, that the proportion of women with anemia in the first country is less than the proportion of women with anemia in the second country? Perform a one-tailed test. Then complete the parts below.Carry your intermediate computations to three or more decimal places and round your answers as specified in the parts below. a. State the null hypothesis H0 and the alternative hypothesis H1. b. Find the values of the test statistic. c. FInd the p-value. d. Can we conclude that the proportion of women with anemia in the first country is less than the proportion of women with anemia in the second country?

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS