{ exp(-5) 203 f (x; 0) : x >0 otherwise where 0 > 0. (a) Find the MLE for 0. (b) Find the MLE for Var (X1). (c) Given X1 compute the realization (observed value) of the MLE you determined in (b). for 8. 56.65, X2 32.15, X3 = 25.71, X4 67.83, X5 61.77,
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- The marginal cost function for the manufacture of wireless headphones is given by: C0(x) = 20 −x200 where x is the number of headphones manufactured. Use a Riemann sum with n = 5 to estimate the cost of producing the first 5 headphones.Solve for y2 by using reduction of order And for nonhomogeneous using undetermined coefficients linear mathematicsThe marginal cost function for the manufacture of headphones is given by: where x is the number of headphones manufactured. Use a Riemann sum with n = 5 toestimate the cost of producing the first 5 headphones.
- Find the marginal PMF of X2. Give an example showing that, even if f0(c) = 0, it could happen that f(x) does not have a localmaximum or minimum at x = c. How is this consistent with Fermat’s Theorem in the book?A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with dimensions 16cm by 30cm by cutting equal squares from the four corners and turning up the sides. Find the function values at the critical number/s and at the endpoints. What is the largest possible volume of the box? What is the length of the side of the cut-out square that will make the box which has the largest possible volume?
- A system consists of two components whose lifetimes (in years) X1, X2 are inde-pendent and identically distributed with pdf f(x) = 0.5e−0.5x, x >0. (a) Show that the mean of X is 2 and use this to find E(X2−2X1). (b) ComputeP(X2= 2X1) andP(X2>2X1). (c) ComputeCov(X1, X2−2X1). You may use the fact that Var(X1) = 4.Find the general solution using Reduction of Order: y''=2lnxfor a series of dependent trials the probablity of success on any traip is (k+1)/(k+2) where k is equal to the number of success on the previous two trials compute lim n->infinity P
- Find the local minima/maxima of -x + ln x if it exist2.Explain why f(x) = x/(x-2) does not have an extreme value on the interval (0,5).Determine the value of x within the interval (0, 1) that minimizes the function f = (x –1)(x –2.5) to within ± 0.025 by .(a) the Fibonacci method and (b) the golden section method.