Let 1 , 2 , be independent r v s having an exponential distribution, and E i 1 Let S 0 0, St 1 t , and X t C t exp S t , where C t is a constant such that X t is a martingale (a) Find C t (b) Find lim t X t How fast is such a convergence ...

a First Ee fo e e dx The reader who did not skip Chapter 8 may just write Eei M 1 1 ...

Let 1 , 2 , ... be independent r.v.s having an exponential distribution, and E{

Question:

Let ξ₁, ξ₂, ... be independent r.v.’s having an exponential distribution, and E{ξ_i} = 1. Let S₀ = 0, St = ξ₁ +...+ξ_t, and X_t = C_t exp{−S_t}, where C_t is a constant such that X_t is a martingale.

(a) Find C_t.

(b) Find lim_t→∞ X_t. How fast is such a convergence?

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Probability And Stochastic Modeling

ISBN: 9781439872062

1st Edition

Authors: Vladimir I. Rotar

See More Books

Question Posted: Jan 11, 2024 09:01 AM

See More Questions

A materials scientist is experimenting with a new material with which to make beverage cans. She fills cans with liquid at room temperature, and then refrigerates them to see how fast they cool....
Wallace and Brace CPA assign a partner to screen and recommend (or decline) potential clients prior to acceptance. Discuss at least 4 specific issues which should have been considered prior to...
Suppose that $\mathrm{x}$ is a linked-list Node. What is the effect of the following code fragment? $t$. next $=x$. next; $x \cdot$ next $=t ;$
Journalizing Various Receivable Transactions the trial balance before adjustment for Sinatra Company shows the following balances. Using the data above, give the journal entries required to record...
A ring of thin wire with active resistance R and inductance L rotates with constant angular velocity w in the external uniform magnetic field perpendicular to the rotation axis. In the process, the...
What are the main elements of power transmission ? Mention them.
Kowalski Company manufactures a number of specialized machine parts. Part Compo-24 uses $35 of direct materials and $15 of direct labor per unit. Kowalskis estimated manufacturing overhead is as...
In the context of bioseparations, what are the latest advancements in chromatographic techniques for purifying biological products, and how do they address issues of throughput, purity, and...
Show directly that in the urn model, the probability of selecting a red ball at the second drawing is the same as at the first.
Let 1 , 2 , ... be independent r.v.s uniformly distributed on [0,a]. Let X 0 = 1 and X t =C t 1 ... t . For which constant C t is X t a martingale?
Assume that a sinusoidal voltage source with a variable frequency and V max = 50 V is applied to the circuit shown in Fig. 12-59. (a) At what frequency f is |I| a minimum? (b) Calculate this minimum...
Olivia and Tatiana form Jen Co. earlier this year. Olivia contributed services worth $24,000 and property worth $1,000 and Tatiana contributed property worth $25,000. Each received 25 shares of Jen...
What is the discount factor that is equivalent to a 5% discount rate?
A friend asks to borrow $54 from you and in return will pay you $57 in one year. If your bank is offering a 5.8% interest rate on deposits and loans: a. How much would you have in one year if you...
Due to your good credit, your bank reduces the interest rate on your $14,000 loan from 9.3% to 7% per year. Thanks to the change, how much will you save in interest this year?
You have $900 and a bank is offering 4% interest on deposits. If you deposit the money in the bank, how much will you have in one year?
The estate tax is a tax on the value of property transferred at death. Why is payment of the estate tax not a common event?
Assume that your audit team has established the following parameters for the examination of ELM's sales transactions: LO G-3 Risk of incorrect acceptance...
What are the challenges posed by strategic information systems, and how should they be addressed? a. List and describe the management challenges posed by strategic information systems. b Explain how...
What ethical, social, and political issues are raised by information systems? a) Explain how ethical, social, and political issues are connected and give some examples. b) List and describe the key...
What specific principles for conduct can be used to guide ethical decisions? a. List and describe the five steps in an ethical analysis. b. Identify and describe six ethical principles.
Instruction: This case study requires you to make a report on Virtual Machine Software. You may choose VMWare, Oracle VM VirtualBox or any other alternative. Tasks: List Australian government and...
What is a virtual machine? 2. What is a Java Virtual Machine? 3. What is Java bytecode? 4. What is the relationship between Java Virtual Machines and Java bytecode? 5. If you were invited to a class...
Highlight the difference between Java Virtual Machine and Dalvik Virtual Machine. Which one of the virtual machines is used in Android Studio to compile android apps?

Let 1 , 2 , ... be independent r.v.s having an exponential distribution, and E{

Question:

Step by Step Answer:

a First Ee fo e e dx The reader who did not skip Chapter 8 may just write Eei M 1 1...View the full answer

Probability And Stochastic Modeling

Students also viewed these Business questions