Problem regarding the accept-reject sampling

Reference no: EM13985283

Here is a method called accept-reject sampling for drawing observa- tions from a distribution.

(a) Suppose that f is some probability density function. Let g be any other density and suppose that f (x) ≤Mg(x) for all x, where M is a known constant. Consider the following algorithm: (step 1): Draw X ∼ g and U ∼ Unif(0, 1); (step 2): If U ≤ f (X)/(Mg(X)) set Y = X, otherwise go back to step

1. (Keep repeating until you ?nally get an observation.) Show that the distribution of Y is f.

(b) Let f be a standard Normal density and let g(x) = 1/(1 + x2) be the Cauchy density. Apply the method in (a) to draw 1,000 observations from the Normal distribution. Draw a histogram of the sample to verify that the sample appears to be Normal.

Reference no: EM13985283

Questions Cloud

Calculate ann and sam''s translational velocities : Calculate Ann and Sam's translational velocities vA and vS and the frequencies fS and fA at which they are spinning.

Determining the axioms of probability : For ?xed B such that P(B) > 0, show that P(·|B) satis?es the axioms of probability.

Writing a law case brief : Writing a Law Case Brief. You do not need to be a Law tutor to do this (I am not a law student and this is an elective course). The assignment can cover any of the following supreme court cases which can be easily accessed online. The specific assign..

Explain what type of data was collected for study : Explain what type of data was collected for this study: nominal, ordinal, interval, or ratio. Describe the sampling methods used to obtain the study sample

Problem regarding the accept-reject sampling : Here is a method called accept-reject sampling for drawing observa- tions from a distribution.

What is the meaning of impracticability within a contract : What is the meaning of impracticability within a contract?

What events would lead to the discharge of a contract : What events would lead to the discharge of a contract?

Compute and compare own price elasticities for all brands : Compute and compare own price elasticities for all the brands. Comment on the results - What are the managerial implications that one can infer from your results? Be specific.

Estimate the density of the ?rst variable : Get the data on fragments of glass collected in forensic work from the book website. Estimate the density of the ?rst variable (refractive in- dex) using a histogram and use a kernel density estimator.

User Account

All Pages