Suppose that the probabilities are0.4, 0.3, 0.2, and 0.1, respectively, that0,1,2 and 3 power failures will hit acertain subdivision in any givenyear. If X represents the no. ofpower failures hitting thissubdivision given g(x) = 5x + 3, findE[g(x).

Answered: Image /qna-images/answer/6d5bd2bd-f2cd-4137-ba97-6bc412cec651.jpg

Answered: Suppose that the probabilities are 0.4,…

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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(d) Experiment: measure the quantities a, b, c (in cm) of rainfall in a day at each of three weather stations A, B and C. Event: it is driest at station A. 2. Suppose we have 2=[0,9]={xR;0
(a) If the sum of the deviations of the numbers X1, X2, X3, ....., Xn from their mean, x, is zero. That is, E1(xi – x) = 0, show if k = x + c, that E-1(x; – k)? = E-1 (x; – x)2 + nc? Li%3D1
3. Let X1, and E- X; are independent. , Xn be iid with exponential distribution with mean 0. Show that (X1+X2)/ E=1 X;
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Prove the following
1. Test whether the following expression is a valid CDF. The range of validity of the variable is 0 to ∞. If it is a valid CDF, obtain the corresponding pdf and its mean. If it is not a valid CDF, test whether it is a valid pdf? If it is a valid pdf, obtain the corresponding CDF and the mean. 2x x² A(x)-[1-exp(-) ++ [¹-exp(-²3)] -+-)] = exp 5 16 x² 8
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3. Suppose X is a discrete random variable with pmf defined as p(x) = log10 ( for %3D x = {1,2,3,...9} Prove that p(x) is a legitimate pmf.
Consider the following scenario: • Let P(C) = 0.3• Let P(D) = 0.8• Let P(C|D) = 0.3 A. P(C AND D) = [ Select ] ["0.30", "0.24", "0.26", "0.11"] B. Are C and D Mutually Exclusive? [ Select ] ["No, they are not Mutually Exclusive.", "Yes, they are Mutually Exclusive."] C. Are C and D independent events?[ Select ]["No, they are Dependent.", "Yes, they are Independent."] D. P(C OR D) = [ Select ] ["0.92", "0.86", "0.60", "1.1"] E. P(D|C) = [ Select ]["0.30", "0.95", "0.24", "0.80"]
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A certain market has both an express checkout line and a superexpress checkout line. Let X, denote the number of customers in line at the express checkout at a particular time of day, and let X, denote the number of customers in line at the superexpress checkout at the same time. Suppose the joint pmf of X, and X, is as given in the accompanying table. X2 1 3 0.09 0.07 0.04 0.00 1 0.05 0.15 0.05 0.04 X1 0.05 0.04 0.10 0.06 0.01 0.02 0.04 0.07 4 0.00 0.02 0.05 0.05 (a) What is P(X, = 1, X, = 1), that is, the probability that there is exactly one customer in each line? P(X, = 1, X, = 1) = | (b) What is P(X, = x,), that is, the probability that the numbers of customers in the two lines are identical? P(X, = X,) = (c) Let A denote the event that there are at least two more customers in one line than in the other line. Express A in terms of X, and X,. O A = {X, 2 2 + X2U X, 2 2 + Xq} O A = {X, s 2 + X2 U Xq 2 2 + Xq} O A = {X, s 2 + X2 U Xq S2+ Xq} O A = {X, 2 2 + X2 U Xq S2+ Xq} Calculate…

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Suppose that the probabilities are 0.4, 0.3, 0.2, and 0.1, respectively, that 0,1,2 and 3 power failures will hit a certain subdivision in any given year. If X represents the no. of power failures hitting this subdivision given g(x) = 5x + 3, find E[g(x)).