answer c & d only Let X be a random sample of size n from N(µ1,0?) and let Y be a random sample ofsize m from N(µ2,03) where X and Y are independent. Determine the distribution of each of thefollowing:Ý - 42(a)Sy/Vm(b)assuming of = o?(X – Y) – (µ1 – z)(c)+т(х — Ү) — (ш — нэ)(d)where S, is the pooled varianceS2

Given X~Nμ1,σ12 with sample size nY~Nμ2,σ22 with sample size m

Answered: answer c & d only

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

Let Y1 < Y2 < · · · < Yn be the order statistics of a random sample of size nfrom a distribution with pdf f(x) = 1, 0 < x < 1, zero elsewhere. Show that thekth order statistic Yk has a beta pdf with parameters α = k and β = n − k + 1.
Let X1,...,Xn be iid exponential(θ) random variables. Derive the LRT of H0 : θ = θ0 versus Ha : θ 6= θ0. Determine an approximate critical value for a size-α test using the large sample approximation.
Let X1, .... Xn be a random sample from a population with location pdf f(x-Q). Show that the order statistics, T(X1, ...., Xn) = (X(1), ... X(n)) are a sufficient statistics for Q and no further reduction is possible?
X is an exponential random variable with λ =1 and Y is a uniform random variable defined on (0, 2). If X and Y are independent, find the PDF of Z = X-Y2
Let Y1 < Y2 < Y3 be the order statistics of a random sample of size 3 froma distribution having the pdf f(x) = 2x, 0 < x < 1, zero elsewhere. Show thatZ1 = Y1/Y2, Z2 = Y2/Y3, and Z3 = Y3 are mutually independent.
Suppose that two random variables X and Y have the joint PDFfXY(u, v) = {60(u^2)v u ≥ 0, v ≥ 0, and u + v ≤ 1, 0 otherwise.(a) Are X and Y independent?(b) What is the marginal distribution fX(t)?(c) What is Pr[X ≥ Y]? (To set up the right integral, it might help you to draw the rangeof (X, Y) in the uv-plane and identify the region within that range where u ≥ v.)
Let Yn denote the nth order statistic of a random sample of size n froma distribution of the continuous type. Find the smallest value of n for which theinequality P(ξ0.9 < Yn) ≥ 0.75 is true.
Consider a real random variable X with zero mean and variance σ2X . Suppose that wecannot directly observe X, but instead we can observe Yt := X + Wt, t ∈ [0, T ], where T > 0 and{Wt : t ∈ R} is a WSS process with zero mean and correlation function RW , uncorrelated with X.Further suppose that we use the following linear estimator to estimate X based on {Yt : t ∈ [0, T ]}:ˆXT =Z T0h(T − θ)Yθ dθ,i.e., we pass the process {Yt} through a causal LTI filter with impulse response h and sample theoutput at time T . We wish to design h to minimize the mean-squared error of the estimate.a. Use the orthogonality principle to write down a necessary and sufficient condition for theoptimal h. (The condition involves h, T , X, {Yt : t ∈ [0, T ]}, ˆXT , etc.)b. Use part a to derive a condition involving the optimal h that has the following form: for allτ ∈ [0, T ],a =Z T0h(θ)(b + c(τ − θ)) dθ,where a and b are constants and c is some function. (You must find a, b, and c in terms ofthe information…
A researcher is interested in testing whether annual house hold income in Philadelphia is normal. So she took a sample of 50 house holds and found that skewness (s)= 2.3190 and Kurtosis (k) = 6.7322. Use the Jarque- Bera Test to test , at alpha 0.05, whether income follows normal distribution. -Yes, population is normal because Chi-Square test is higher than critical value. -Yes, population is normal because Chi-Square test is less than critical value. -No, population is not normal because Chi-Square test is higher than critical value. -No, population is not normal because Chi-Square test is less than critical value.
Let X1, X2,...Xn be a random sample of size n from a normal distribution with mean u and variance o2. Let Xn denote the sample average, defined in the usual way. PROVE E [Xn] = u
The random variable X has a Bernoulli distribution with parameter p. A random sampleX1, X2, . . . , Xn of size n is taken of X. Show that the sample proportionX1 + X2 + · · · + Xnnis a minimum variance unbiased estimator of p.Given that X1, X2, . . . , Xn forms a random sample of size n from a geometric population withparameter p, show thatY =n∑j=1
1.- A study conducted in the automotive field states that more than 40% of vehicle engine failures are due to problems in the cooling system. To test this statement, a study is carried out on 70 vehicles and the critical region is defined as x < 26, where x is the number of vehicle engines that have problems in the cooling system. (use the normal approximation)a) Evaluate the probability of making a type I error, assuming that p = 0.4.b) Evaluate the probability of committing a type II error, for the alternative p = 0.3.

SEE MORE QUESTIONS

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS