Find the CDF and PDF of T.
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Q: (a) Var(X + Y ) = Var(X)+ Var(Y) (b) Ε(XY) - (EX) (EYΥ) (c) E(X + Y ) = EX+ EY
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For 80% of lectures, Professor X arrives on time and starts lecturing with delay T = 0. When Professor X is late, the starting time delay T is uniformly distributed between 0 and 300 seconds. Find the CDF and
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- Consider randomly selecting n segments of pipe and determining the corrosion loss (mm) in the wall thickness for each one. Denote these corrosion losses by Y₁' Yn. The article "A Probabilistic Model for a Gas Explosion Due to Leakages in the Grey Cast Iron Gas Mains"+ proposes a linear corrosion model: Y; = t;R, where t; is the age of the pipe and R, the corrosion rate, is exponentially distributed with parameter 1. Obtain the maximum likelihood estimator of the exponential parameter (the resulting mle appears in the cited article). [Hint: If c> 0 and X has an exponential distribution, so does cX.] O Â = O Â = O λ = * * O n Srit) i = 1 n j = 1 Σ i = 1 n n i = 1 n LY i = 1 n 0 1 = L (rt) 2 i = 1 | = 1 n n Y; | = 1Calculate the residual of P = (1.2, 2.4) with respect to the line 3x + 4y = 12.The length of time in minutes X that a customer spends in line at a bank before being served is described by the pdf f(x)=0.2e-0.2x, x≥0 What is the probability that a customer will wait more than 10 minutes?
- Find the rate at which the total average number of COVID cases is increasing at x=15 tents and dxdt=1 tent per day, Given that if 25 tents are built, the average number of COVID cases per tent will be 6 cases while the average number of cases will increase by 2 per tent for each additional tent in the same area due to overcrowding.NOTE: DO NOT USE PIECEWISE FUNCTIONLet C(t)=0.029t2+0.214t+53.291 be the capacity (in percent) at which U.S. nuclear power plants are working t years after 1970. A) Estimate at what capacity (in percentage) U.S. nuclear power plants were working in 1995. B) Predict in which year U.S. nuclear power plants will be working at full (100%) capacity. Thank you so very much for the help.Suppose that the p.d.f. of X is as given f(x)=4x-1 for 0≤x≤1 and 0 otherwise Find the pdf of Y=X1/2.
- Roll two dice and observe the numbers coming up. Define two events by: A="the sum is six," and B-"the numbers are not equal." Find and compare P(B) and P(BIA).8. Define cumulant generating function. Obtain a relationship between cumulants and moments.Q3 (4 pts): Determine whether the Mean Value Theorem applies on the given interval. If so, find the point(s) that are guaranteed to exist by the Mean Value Theorem. f(x) = 3x² + 2x+5 [−1,1]
