3 Let X be a Poisson with parameter 1. Prove (step by step) that P(X < 4) = edr. 1 p³e¬²dx.
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- Use Simpson's 3/8 rule to compute the approximated solution where f (x) = 1/Cosx + 4 defined at the interval (1,4.5) and n = 7Let f(x) = 1/[π(1 + x2)], −∞< x < ∞ be the pdf of the Cauchy random variable X. Showthat E (X) does not exist. (hint: split into two integrals (−∞,0) and (0,∞))If X is exponentially distributed with parameter λ and Y is uniformly distributed on the interval [a, b], what is the moment generating function of X + 2Y ?
- Assume that your computer completes a 5000 equation back substitution in 0.005 seconds. Use the approximate operation counts n2 for back substitution and 2n3/3 for elimination to estimate how long it will take to do a complete Gaussian Elimination of this size. Round your answer to the nearest second.Consider the seriesxt = sin(2πU t),t = 1, 2, . . ., where U has a uniform distribution on the interval (0, 1). Prove xt is weakly stationaryA rectangular plate with insulated surface is 10 cm. wide and so long compared to its width that it may be considered infinite length. If the temperature along short edge y = 0 is given u(x,0) = 8 sin(px/ 10) when 0 <x <10, while the two long edges x = 0 and x = 10 as well as the other short edge are kept at 0o C, find the steady state temperature distribution u(x,y).
- integral of C(1-e^(-bt)) with the initial time being 0Find the fourth-order Taylor Series approximation of y = cosx + sinx at x = 0.1 on the basis of the value of y and its derivative at X0 = 0. Compute also for the percent relative error.Find the normal line to f(x)=ax^2-3ax at x=2. Assume that a is a positive constant.