5. Suppose that X,, X2, -, Xm and Y1,Y2, ,Y, are independent random samples from N(Hx,o)and N(Hy, o), respectively.a. Find E(X – Ý).b. Find V(X – Ý)

Given that, X1,X2...Xm~ N(μx, σx2) Mean of X1,X2....Xm is x̄ and it follows normal distribution with…

Answered: 5. Suppose that X1,X2, ,Xm and Y1, Y2,…

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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1. Let y1,.. , Yn be a random sample from a uniform distribution on the interval (0, B). Let B1 2 Li=1 Yi and B, = ) Max(y1,.., Yn) be estimators for B. Find the sampling distribution of B2 Show that B, and B, are unbiased estimators for B. 11.
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)
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Let X1, X2, ... ,Xn form a random sample from U(0,0). Find minimal sufficient statistics.
11. Let (y1, Y2 ... Yn) be independent random sample from the uniform distribution on [0, 1]. (a) show that Z = – In Y; has exponential distribution with parameter 1. (b) Hence or otherwise, show that -2 In Y; xản
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Is the following statements correct or incorrect: Suppose that a random vector Y' = (Y1, Y2, Y3) has multi-normal distribution with mean vector u and variance-covariance matrix £ given by and Σ 흑 0 1 respectively. CH), Then the distribution of Z = Y is N 1
Assume that M= N(h)+k, h² + k, h* + ... Use the following data to find N,(). N,(h)=2.451, N,G)=2.896, N,)=3.285, N,(- = 3.786, N,()= 4.422 16 O a. 4.634 O b. 4.287 O c. 3.044 O d. 3.4146 O e. 3.953 O f. 5.058 Og. 3.674
1. Given that X~N(39,32)A Random variable X is normally distributed and has a mean of 9 C Random variable X is not normally distributed and the mean is 39 B Random variable X is normally distributed and has a mean of 3 D Random variable X is normally distributed and the mean is 39
24. Gaussian random variables X, and X,, for which, X, = 2, o = 9, X, =-1, ox, = 4 and Cxx, =-3, are transformed to new random variables Y, and Y, according to जापर डेरें| Y, =-X, + X, Y, =-2X,- 3X, (iii) Cy,Cy, .. Find
3. An urn contains exactly 10 red chips and 6 blue chips. Five chips are randomly selected without replacement. Let X denote the number of blue chips in the sample of five chips. (a) What type of random variable is X? Indicate both the type and the appropriate parameters using the "~" notation. Write down the pmf of X, and do not forget to indicate the range of values that x can take on. X ~ px (x) (b) What is the probability that there are between two and four blue chips among the five chosen chips? Express your answer as a decimal. = (*)*

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5. Suppose that X1,X2, ,Xm and Y1, Y2, ,Y, are independent random samples from N(ux,o) and N(uy, o), respectively. a. Find E(X - Y). b. Find V(X - Y)