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If you have any doubt or need more clarification at any step please comment.
Let f: a, b R be a function, continuous on a, b and differentiable on (a,...
Give algorithms for generating random variables from the following distributions. b. 1-2 if 0<<1
Using the result of exercise 7(see question 7 below), give
algorithms for generating random variables from the following
distributions.
b.
1-2 if 0<<1 7. (The Composition Method) Suppose it is relatively easy to generate random variables from any of the distributions F,,-I, . . . , n. How could we generate a random variable having the distribution function 12 i-1 where p,, -1.... . n, are nonnegative numbers whose sum is 1?
max{a1, a2, n<3 Show that 1 1 1 7 . 3 (a1a +.an) 3 an 3 a2 3- a1 using definition of convex
There are 30 people that donated to a church. The amount each person donated has probability density function Find out the probability that exactly 5 people donated between 20 and 30. ,(1)-(*(50-r), (50-x), ifo ifo < x < 50 otherwise TA
Consider a potential well, whose potential is given by (a) Evaluate the reflection and transmission coefficient for the case E > 0. (b) Use your result for the transmission coefficient obtained in (a) above, to evaluate the transmission coefficient for the potential barrier, (V0 > 0) for the case E < V0. Please show all steps thoroughly S-V, (-a <r <a) 10, elsewhere JV, (-a <r <a) V.C) = 0. elsewhere
11. Let X follow possion distribution(µ) a) Show that where h is a function. b) Use the above identity to find the 2nd and 3rd moments. c) Show that EX (h(2)) = E(h(x + 1)) E(X(X - 1)(x - 2)...(X-k+1)) = uk where k > 0
Let be the distribution
function defined by
Let be the
Lebesgue-Stieltjes measure asociated to .
Determine the measurements of the fpllowing sets:
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2. Let f: R R be a continuous function. Suppose that f is differentiable on R\{0} and that there exists an L e R such that lim,of,(z) = L. Prove that f is differentiable at 1-0 with f,(0) = L. (Hint: Use the definition of derivative and then use mean value theorem)
2. Let f: R R be a continuous function. Suppose that f is differentiable on R\{0} and that there exists an L e R such that lim,of,(z) =...
Let f be a differentiable function on R. Assume f' is continuous and always positive. You are searching for a root of f using Newton's method (see Tutorial 5). Your first guess is Xo ER and you compute subsequent guesses as follows: In EN, 2n+1 = In - f(2n) f'(x Let & E R. Prove that IF {Xn}"-o converges to & THEN x is a root of f.
1) Suppose f (a, b) R is continuous. The Carathéodory Theorem says that f(x) is differentiable at -cE (a, b) if 3 (a, b)-R which is continuous, and so that, (a) Show, for any constant a and continuous function (x), that af(x) is continuous at z-c by finding a Carathéodory function Paf(x). (b) Show, for any constants a, B, that if g : (a, b) -R is differentiable at c, with Carathéodory function pg(z), then the linear combination of functions,...