Problem 6 Let X₁, X2, X20 be a random sample of size n = 20 from an No (μ, E) population. Specify eachof the following completely.(a) The distribution of (X₁- )'E-¹(X₁-μ)(b) The distribution of X and √n(X-μ)(c) The distribution of (n-1)S(d) The distribution of n(X-μ)'E-¹(X-μ)

Let X1,X2,.......X20 be a random sample of size n = 20 from an population.

Answered: Problem 6 Let X₁, X2, X20 be a random…

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

4. Question 4: Y is a discrete random variable with PMF S1/3, y=1 p(y) = 2/3, y = 2 (a) Find the MGF for Y. (b) Develop the first two raw moments from MGF and find the variance V(Y). Answers:
12#
9. Zero-mean Gaussian random variables x and y have variance oz= 3 and o= 4 respectively and a y -1 correlation coefficient p = ing Write an expression for the joint density function.
Question 5 Suppose X is a normal random variable with mean and variance o². (i) If a and b are constants, show that aX + b has a normal distribution and find its mean and variance. (ii) If Z = (X − μ)/o, deduce that Z~ N(0, 1). (iii) Using (ii) find P(X 0 is a constant, show that P(µ – co < X < μ+co) does not depend on μ or o.
2
Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
#1. A random sample is to be selected from a normal population with µ= 120 and o=21. (a) Determine the mean and standard deviation of the sampling distribution of xwhen n = (b) How large would n have to be to for o- to be less than or equal to 2.0? = 49.
16. Let X, X2 X, be a random sample from a normal distribution, X, N(6, 25), and denote by X and S2 the sample mean and sample variance. Use tables from Appendix C to find each of the following: (a) P[3 < X < T. (b) P[L860< 3(X-6)/S]. (c) PIS <319375]
25. Suppose X is a random variable distributed with mean u and standard deviation a > 0. If the random variable Y is defined as Y = u(X - uX)/a, then E(Y) is: a. 0 b. 1 d. E(X)
4.2 The probability distribution of the discrete random variable X is f(x) = 3 (*)*** Find the mean of X. 3-x (¹)ª (²³)³—ª, x = 0, 1, 2, 3.
(5) If Xis a r.v. with mean u and variance o?, using Chebyshev's-Inequality, AX-2 20) S (a) 0.5 (b) 0.05 (c)0.657 (d) 0.25.
4-52. If f(x) =e ,- co

SEE MORE QUESTIONS

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

Problem 6 Let X₁, X2, X20 be a random sample of size n = 20 from an No(u, Σ) population. Specify each of the following completely. (a) The distribution of (X₁-μ)'E-¹(X₁-μ) (b) The distribution of X and √n(X-μ) (c) The distribution of (n-1)S (d) The distribution of n(X-μ)'E-¹(X-μ)