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
Here g==h
g(x) = h(x)
11. Let X follow possion distribution(µ) a) Show that where h is a function. b) Use the above identity to find the 2nd...
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?
3. Let U-Bt- tB be Brownian bridge on [0, 1], where {BiJosesi is a Brownian process (i) Show E(Ut0 (ii) Show Cov(U,, Ut) s(1- t) for 0 s ts1. (ii) Let Xg(t)B Find functions g and h such that X, has the same covariance as a Brownian bridge.
3. Let U-Bt- tB be Brownian bridge on [0, 1], where {BiJosesi is a Brownian process (i) Show E(Ut0 (ii) Show Cov(U,, Ut) s(1- t) for 0 s ts1. (ii) Let Xg(t)B...