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Suppose we have a method for simulating random variables from the distributions F1 and F2. Explain how to simulate from the distribution
Give a method for simulating from
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A First Course in Probability (10th Edition)
- Show that variance o? = (x²) – ((x))²arrow_forward3(8x – x²) Determine the mean and variance of the random variable for f(x) = 0arrow_forwardBy hand solution needed onlyarrow_forward7. Calculate the variance of g (X) = 2X + 3, where X is a random variable with probability distribution X 0 1 2 3 f(x)=1/ 4 1180 31100 1 2 8 First, we find the mean of the random variable 2X + 3.arrow_forwardLet X1, X2, ..., X, be independent random variables and Y = min{X1, X2, ..., Xm}. Fy (y) = 1 – || (1 – Fx,(y)) i=1 (a) A certain electronic device uses 5 batteries, with each battery to have a life that is exponentially distributed with mean of 48 hours and is independent of the life of other batteries. If the device fails as soon as at least one of its batteries fail, what is the expected life of the device?arrow_forwardProb. 3 Let X be a random variable with cumulative distribution function (cdf) given by (1-e-x², x ≥ 0 ={1,- x<0 Find the probability that the random variable X falls within one standard deviation of its mean. Fx (x) =arrow_forwardLet X1 and X2 be two independent random variables with common mean E(X1) = E(X2) = µ. The variance of X1 is 1 and the variance of X2 is 16. Consider estimators of u described by û = W1X1 + W2X2 for some constants w1 and w2 that you can choose. (a) Say that w2 the estimate unbiased for all w1? = a – bw1 for some constants a and b. What values of a and b would makearrow_forwardIf the discrete random variable X takes on the values 1 , 2 , 3 and if P ( X = 1 ) = P ( X = 3 ) = 0.2 then the mean of x =arrow_forwardShow that the characteristic function of a Gaussian random variable with zero mean and variance o² is (= x (@) = exp -0² w² 2arrow_forwardThe manager of a bakery knows that the number of chocolate cakes he can sell on any given day is a random variable with probability mass function Px (0) 12 Px(1) = Px (2) = Px(3) Px(4) Px (5) 12 He also knows that there is a profit of $1.00 on each cake that he sells and a loss (due to spoilage) of $0.50 on each cake that he does not sell. Assuming that each cake can be sold only on the day it is made, how many chocolate cakes should he bake to maximize his expected profit? || || ||arrow_forwardthe maximum likelihood estimator of a random variable x with uniform distribution U(0, 0), 0 = max(x₁.x). Is the estimator biased?arrow_forwardThe p.d.f. of a random variable X' is as shown in the figure. The pdf is zero for X 5. Calculate (i) the maximum value of p.d.f. (ii) expectation of X, E(X) (iii) variance of X. fx (x) karrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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