Question

Could u show me how to do part a and c please?

For s > 0, t > 0, Bls, t) =お2.s-1(1-2)t-1 dr is called the beta function and there is the identity B(s, t)- (a) Prove this result for the case that s and t are integers. (Use inte- gration by parts and induction.) (b) Using Matlab (or other software) commands beta and gamma), look up B(st) and verify the identity for s = 1.13 and t = 4.7. (c) Now, estimate B( 1.13.4.7) = rJ3(1-r)3.7 dr using either simple sampling or the hit or miss (your choice). Do this by performing 100 samples and then continuing to generate samples (if necessary) stopping when the estimated standard deviation of the estimator is less than 001. Gie the estinat der sampaks mopuired.

Answer 1

here in part a, i am using the integration by parts and beta function which are given above. for part c we will use MCMC techniques which is best to estimate such type of integration. i will perform part c by using R sofyware but i will describe all steps which i will used. $yonca \z..い-w.teN rm of beto funeton nous, dplocing mtn2 gp/ mtn 1$here it is not easy to use for or while loop therefore we will use hit or miss method for start n=100, using R software

> n=100 > x= (p"0.13" (1-p) ^3.7) sd [11 0.01772045 >#now n=300 > n=300 [1 0.01109033
here note that x is random then values may be some random but will be approximately equal. therefore we can choose n=320 and estimated value of beta fn is 0.1601375.

Any doubt please ask by comment i will respond you and please give your good rating to answer for providing best quality answers in future.