X(t) = Z(t)-2λ h(t) = e¯u(t) Y(t) Ry) = ((f+)943] Z(t) is a sequence of Poisson impulses. λ is the expected number of impulses per unit time. Find a) E[Y(t)] b) R(T)
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- he life X (in years) of a voltage regulator of a car has the pdf f(x) = cx²e-()³, x>0 (b) Find IQR. (a) Find c. (c) Given that it has lasted at least 7 years, what is the conditional probability that it will last at least another 3.5 years? If the moment-generating function of a random variable W is M(t) = (1 - 7t)-20, find the pdf, mean, variance, and mode of W.Let Mx (t) = 1/(1-t), t < 1 be the moment-generating function of a random variable X. Find the moment-generating function of the random variable Y = 2X +1.find P( C|D')
- Let N(t) be the percentage of a state population infected with a flu virus on week t of an epidemic. What percentage is likely to be infected in week 4 if N(3) = 8 and N'(3) = 1.2?x(t) == ()-1 h(t)=pt .u(t) y(t) Z(t) is a sequence of Poisson impulses. X is the expected number of impulses per Find a unit time E[Ÿ(t)] b) Ryy (T).. c) Syy (w)iid 2. Let Y1,..., Yn-1 xỉ and consider U = E Y;. (a) Show that U ~ Xn-1: (b) What is the expectation of U? (c) If o? is a constant, what is the expectation of U?
- A random process X(t) is applied as input to a system whose impulse response is h(t) 3u(t)t² exp (-8t). If E[X(t)] = 2, what is the mean value of the system response y(t). - CS Scanned with CamScannerSuppose the random variable T is the length of life of an object (possibly the lifetime of an electrical component or of a subject given a particular treatment). The hazard function hr(t) associated with the random variable T is defined by hr(t) = lims-o- P(t ≤ T