Σp(1=n)*2- If X1, X2,,...., Xn are independent identically distributedrandom variables with finite expectation, andnS=Σk=1XKthen,E(xk|Sn) =Snk=1,..., n.nwith the very best wishes

Given the independent identically distributed (i.i.d.) random variables x1,x2,...,xn with a…

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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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A docs.google.com/forms/d/e (1) Let X be a random variable with p.d.f. fx) =- , then O.w (b) k- (0) k = (a) k=1 (d) k-5 (e) None of these a is the correct answer b is the correct answer c is the correct answer d is the correct answer e is the correct answer (2) Let X be a random variable with a function x= 0,1, 2,3 4 x! (3-x)! f(x) = , then p(x<1) is 0.w (b) (d) (e) None of these 27 (a) 27 (c) 27 a is the correct answer b is the correct answer c is the correct answer d is the correct answer e is the correct answer
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sar Suppose that we also have the following. E(X)=-5 E(Y)=8 E(Z)=6 Var (X)=24 Var (Y) = 16 Var (Z) = 33 Compute the values of the expressions below. E (4Y+4)= 36 E(-4Z+2X)- -3 = 11.33 Var (4Y)-2= 254 E(-x²) = 49 0|0 X
5 Both K and M has standard normal distribution and they are independent random variables. Z=K+M Find E[K(K^2+M)^(1/4)].
9. Given that f(x, y) = (2x+2y)/2k if x = 0,1 and y = 1,4, is a joint probability distribution function for the random variables X and Y. Find: (f(x|y = 1)
Let X(1), X(2), ..., X(n) be the order statistics of a set of n independent uniform (0, 1) random variables.Find the conditional distribution of X(n) given that X(1) = s(1), X(2) = s(2), ..., X(n-1)=s(n-1).
A bank has 3 counter desks and a very large waiting lounge (assume infinite queue). Customers arrive with a mean of 20 per hour and each desk serves with mean 10 customers per hour, where both rates are exponential. Determine the following : (a) Determine An, tn, C, and Aeff for n = 0, 1, 2, 3... (b) The steady-state probabilities pn,n = 0, 1, 2, 3.. (c) Calculate steady-state measures Ls, Ws, Lq, Wq, c and utilization ratio.
10. Two random variables X and Y take on the values i and 2 with probability 1/2' (i = 1,2, ...). Show that the probabilities sum to one. Find the expected value of X and Y.
(1) Let X be a random variable with p.d.f. ke 3 0
Let Y1, Y2, Y3 denote independent exponential random variables with respective rates A; for i e {1,2, 3}. Answer the following questions; (a) Compute E[Y1 +Y2 +Y3]Y1 > 1, Y2 > 2, Y3 > 3]. Your answer should be an expression using A;'s. (b) Compute the probability that Yı is the smallest among three random variables. Hint: P(X < Y) = S" Px,y (x, y)dædy where Px,Y (x, y) is the joint density function.
Suppose that X is a random variable * ? having the following m.g.f., Find Var(x) 7t_e4t M, (t) = eT 173 O 5 O 413 O 3148 O 55 O
A bank has 3 counter desks and a very large waiting lounge (assume infinite queue). Customers arrive with a mean of 20 per hour and each desk serves with mean 10 customers per hour, where both rates are exponential. Determine the following : (a) Determine An, tn, C, and Aeff for n = 0, 1, 2, 3... (b) The steady-state probabilities pn,n = 0, 1, 2, 3.. (c) Calculate steady-state measures Ls, Ws, Lg, Wq, c and utilization ratio.
4 of these 1 5 of these 3 of (a) 1.0211 (c) 1.5207 (e) 1.2962 these 2 (a) 0.1111 (c) 2.3333 (e) 12.9375 2 of these 16 tickets total 3 FIG. 5. 2 of these 26. Let X be the random variables described in Fig- ure 5. Find E(√x + 1). (b) 2.3125 (d) 0.4613 X Random draw from the box 27. Let X be the random variable described in Figure 5. Find E(X³ | X < 2). (b) 0.5625 (d) 1.3125

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Σp(1=n)* 2- If X1, X2,,...., Xn are independent identically distributed random variables with finite expectation, and n S= Σ k=1 XK then, E(xk|Sn) = Sn k=1,..., n. n with the very best wishes