X (4) is a WSS process with E [X (t)]=2 and Ryx (T) = 4 + e- 0.1 la, Find the mean 1 and variance of S = / x (1) - dt
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![X (1) is a WSS process with E [X (t)] =2 and Ryx (T) = 4 + e- 0.1 la, Find the mean
and variance of S =/x () dt
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- The power density spectrum of a WSS process is Sy (ω) -4πδ(ω) +3π δ(ω - 5π) + 3 πδ(ω+ 5π) +2π δ(ω- 4) + 2πδ(ω+ 4) (a) What are the frequencies in X(t) ? (b) Find mean variance and average power of X(t).Given the pdf: f(x) = { (1/6)e^(1/6x) ; x > 0 0; ew] (i) Find the mean and variance of X using the pdf. (ii) Find the moment generating function of X. (iii) Find the mean and variance of X using the moment generating function.If X is an exponential random variables with rate 1, then its distribution function is given by F(x) = 1 − e−x Show that x = − ln(1 − u).
- Derive the following:(a) cumulative distribution function(b) meanY has a distribution function (0, ys0, 24 F(y) = 0A WSS process X (t), with mean value 5 and power spectrum Sxx (@) = 50 n. 8 (@) + is applied to a network with impulse response %3D 1+ 2. h (t) = 4. e-4 I %3D (a) Find H (@) of the network (b) Find the Mean and power spectrum of the response Y (t). 3/2Which of the following could be the correlation function of a stationary random process? (a) R(t) = exp(-7). (d) R(T) = sin(7). (b) R,(t) exp(-г)и( г). (e) R(7) = cos (r). %3D (c) R (7) = exp(l1). (f) R(7) = sinc(7). %3DQ5 Find the variance for the PDF px(x) = e-«/2, x > 0.You test some components with a Weibull distribution at temperatures of 100 Celcius and 60 Celcius. At those temperatures you estimate a characteristic life of 15000 hours and 25000 hours respectively. hint: Boltzmann's constant is k = 8.617 x 10-5. Temperature in Celcius + 273.15 = temperature in Kelvin. If n is an integer, T(n) = (n – 1) a) Using linear regression, estimate the Arrhenius model parameters A and AH. b) Give the MTTF, median, and 90th percentile at T = 20 Celcius. Assume that the shape parameter is 0.51. Fix r € N, and suppose that Y₁,..., Yn are independent and identically distributed NegBin(r, ) random variables, each with probability mass function given by ¡v (u | 0) – (1 + r − ¹) (1 - fy y (1 - 0) ³0⁰ for y ¤ N and unknown 0 € (0, 1). Here the number of successes r in the negative binomial is known.3) Assume that a random variable X has moment generating function as follows: e' + e²¹ M(t)=4-2e¹ ∞ Calculate the mean and variance of X. for tCalculate correlation and probable error between physical parameters (temperature and humidity) Number of families(x)=2 Number of sites(n)= 1 Temperature(y) in autumn= 24.1 Humidity(y) in autumn= 35 20 1 19 Calculate correlation and probable error between physical parameters (temperature and humidity) Using the following formula coefficient of correlation (r). r = n([xy)-([x) (Ey) V[n(Ex 2)-(Ex) 2][n(Ey2)-([y) 2] ISEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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