could you give me a more detailed answer ? 4. Let Y be a positive-valued random variable, i.e., fy (y) = 0 for y < 0E(Y)4.1 Let a be any positive constant, and show that P(Y > a) <22 (Markovainequality) -4.2 Let X be any random variable with variance o?, define Y =(X-E[X])2 and a =e? for some ɛ. Obviously, the conditions of the problem are satisfied for Y and a aschosen here Derive the Chebychev inequalityP(|X – E(X)| > €) <e2Answer:E[Y] = ° yfr(y)dy > yfr(y)dy> a f, yfr(y)dy = aP(Y > a)Thus P(Y α) < E[Υ]/α.2) Clearly P(|X – E[X]| > €) = P((X – E[X])² > e?). Thus using the results of the previous questionwe obtainE[(X – E[X])²]E2P(|X – E[X]| > €) = P ((X – E[X])² > e?) <

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4. Let Y be a positive-valued random variable, 1.e., Jy E(Y) 4.1 Let a be any positive constant, and show that P(Y > a) < (Markov a inequality) 4.2 Let X be any random variable with variance o?, define Y =(X-E[X])2 and a = e2 for some ɛ. Obviously, the conditions of the problem are satisfied for Y and a as chosen here Derive the Chebychev inequality e

4. Let Y be a positive-valued random variable, 1.e., Jy E(Y) 4.1 Let a be any positive constant, and show that P(Y > a) < (Markov a inequality) 4.2 Let X be any random variable with variance o?, define Y =(X-E[X])2 and a = e2 for some ɛ. Obviously, the conditions of the problem are satisfied for Y and a as chosen here Derive the Chebychev inequality e

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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Suppose Xn is an IID Gaussian process, withµX[n]=1, and σ2 X[n]=1Now, another stochastic process Yn = Xn − Xn−1. Please find:(a) The mean µY (n).(b) The variance σ2Y (n).(c) The auto-correlation RY (n, k)
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Consider the time series xt = β1 + β2t + wt, where β1 and β2 are known constants and wt is a white noise process with variance σ2 w. (a) Determine whether xt is stationary. (b) Show that the process yt = xt − xt−1 is stationary. (c) Show that the mean of the moving average vt = 1 2q + 1 q j=−q xt−j is β1 + β2t, and give a simplified expression for the autocovariance function.
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A child gets a weekly allowance (a certain non-negative number of dollars). The amount (in dollars) is random with expectation equal to 6 and variance equal to 6. Let’s denote this random variable by X. I want to estimate (from above) the chances that the child gets 10 dollars or more on a given week. In other words, I want to find c such that P(X ≥ 10) ≤ c, with c that is as small as possible.(a) Use the Markov inequality to find c such that P(X ≥ 10) ≤ c.(b) Use the Chebyshev inequality for the variance to find c such that P(X ≥ 10) ≤ c.(c) Read about the one-sided Chebyshev inequality, and use it to find c such that P(X ≥ 10) ≤ c.
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