Please do both (a) and (b) and fully explain in detail.
Please do both (a) and (b) and fully explain in detail. Problem 4. Chernoff bound for...
a b and c please
and thankyou
Problem 2 Let X is a random variable with Poisson distribution X ~ Poisson(λ), (a) Find E(X1X2 i). λ > 0. 、 (b) Find E(xIx2). (c)Prove that λ>2-2a-ka for λ>0.
Please explain with as much detail as possible and write as
clear as possible please.
Problem 3: Obtain v(t) fort > 0 in the circuit below 10Ω t=0 120 V (コ 4 H
Q1. Assume that X is a continuous and nonnegative random variable with the cumulative distribution function F and density f. Let b>0. (a) Write the forinula for E(X b)+1. (b) Apply the general formula from (a) to exponential distribution with parameter λ > 0.
Please explain in full detail.
6. (20) Fill in the missing reagents to accomplish these conversions >1 step may be needed):
Let X be an exponentially distributed random variable with parameter λ. Prove that P(X > s + tK > t) P(X > s) for any S,12 0
Problem 2. This problem investigates the similarity between the geometric and ex- ponential random variables observed last week. Let Y be a geometric random variable with parameter p, so that Y represents the trial number of the first success in a sequence of independent Bernoulli trials. Suppose the trials occur at times , 2, . . . , and that δ and p are both very small. Let λ /δ. At time t, about t/6 trials have taken place (a)...
4. Find the Fisher Information and the Cramer-Rao lower bound for the variance of an unbiased estimator of θ given a random sample . , xn from the density r3 -z/θ where x > 0 and f(x:0-6 94e θ > 0.
Q2. Assume that X is a continuous and nonnegative random variable with the cumulative distribution function Fx Let b> 0. (a) Find the cumulative distribution function of Y = XI(X < b} (b) Apply the general formula from (a) to exponential distribution with parameter λ > 0.
3) Using the Method of Variation of Parameter, solve the following linear differential equation y' (1/t) y 3cos (2t), t > 0, and show that y (t) 2 for large t
Problem 1. Let X be a contiuous random variable with probability density 2T f0SS Let A be the event that X > 1/2. Compute EXA) and Var(XA).