Learning Materials
Features
Discover
Chapter 10: Q. 10.11 (page 431)
Use the rejection method with g(x) = 1, 0 < x < 1, to determine an algorithm for simulating a random variable having density function
The algorithm is generate(which is unform) and take random number.
Over 30 million students worldwide already upgrade their learning with 91影视!
All the tools & learning materials you need for study success - in one app.
Get started for free
Suppose it is relatively easy to simulate from Fi for each i = 1, ... , n. How can we simulate from
(a)
(b)
Give an efficient algorithm to simulate the value of a random variable with probability mass function
p1 = .15 p2 = .2 p3 = .35 p4 = .30
In Example 4a, we showed that
E[(1 鈭� V2) 1/2] = E[(1 鈭� U2) 1/2] = 蟺/4
when V is uniform (鈭�1, 1) and U is uniform (0, 1). Now show that
Var[(1 鈭� V2) 1/2] = Var[(1 鈭� U2) 1/2]
and find their common value.
The following algorithm will generate a random permutation of the elements 1, 2, ... , n. It is somewhat faster than the one presented in Example 1a but is such that no position is fixed until the algorithm ends. In this algorithm, P(i) can be interpreted as the element in position i. Step 1. Set k = 1. Step 2. Set P(1) = 1. Step 3. If k = n, stop. Otherwise, let k = k + 1. Step 4. Generate a random number U and let P(k) = P([kU] + 1) P([kU] + 1) = k Go to step 3. (a) Explain in words what the algorithm is doing. (b) Show that at iteration k鈥攖hat is, when the value of P(k) is initially set鈥擯(1),P(2), ... ,P(k) is a random permutation of 1, 2, ... , k.
Explain how you could use random numbers to approximate , where k(x) is an arbitrary function.
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine