Consider the following algorithm generating a random variable X in pseudocode. % denotes a comment that is not part of the code.R = RAND(0,1) % a random uniformly distributed number R between 0 and 1 is chosenX = 2R % X is calculated with this formula.Then the random variable X generated by this code has the distribution with probability density function given by:f (x) =2{x,0,f (x) =x^4,0

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Answered: Consider the following algorithm…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Exercise 4 Suppose X and Y are independent random variables such that X has uniform (0, 1) distribution, Y has exponential distribution with mean 1. b) E(XY) c) E[(X - Y)²] d) E(X²e²Y)
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85% of tax returns have computational errors. This means that if we randomly select a tax return, there is a probability of 0.85 that the tax return will have at least one computational error. Whether one tax return has a computational error is independent of whether any other tax return has a computational error. John Jay, a new tax return auditor randomly selects tax returns for audit one after another. Let X = the number of tax returns selected until he selects the 1st return with computational errors. Let Y = the number of tax returns selected until he selects the 2nd return with computational errors. What is the probability that the 1st 3 tax returns selected have computational errors? What is the expected value of X? What is the variance of X? What is the probability that X > 3? What is the probability that X < 3? What is the probability that Y = 4? What is the probability that Y< 4?
Let X and Y are independent Poisson random variables such that E(X) = E(Y)=2. Let Z=X+Y. Compute P(X=2|Z=3).
Let Y be a discrete random variable with generating function 4 Gy (s) 6 - s What is E(Y) (in decimal)? Answer:
Let X denote the number of bits received in error in a digital communication channel, and assume that X is a binomial random variable with p = 0.01. If 100 bits are transmitted, then P(X>1)=
A random variable X has the following probability mass function for x = 0, 1, 2, 5. Based (PMF): P(X= x) = (x+1) 12 on this PMF, what is P(X≥ 2)? 5/12 1/2 3/4 11/12
The probability generating function for a random variable X is given by: 1 1,25 1 9x(z) =z2 + 1 -z20 710 + 2 P(X < 5 |X < 13) equals Select one: а. 0.8 b. 0.2 C. 1 d. 0.286 е. О
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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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