--%>
Assignment Help - homework help

Use the law of iterated expectation to calculate

Suppose we have a stick of length L. We break it once at some point X _ Unif(0;L). Then we break it again at some point Y _ Unif(0;X). Use the law of iterated expectation to calculate E[Y ].

 

E

Expert

Verified

X is the length of the stick after we break for the ?rst time. Y is the length after the second time.

We have E[ Y | X ] = X /2, since the breakpoint is chosen uniformly over the length X  of the remaining stick.  similarly, E[X ] = L/2.

E[Y] = E[E [Y | X ] ]= E[X/2]=E[X]/2 = L/4

 

 

   Related Questions in Advanced Statistics

  • Q : Probability Distributions and Data

    1. A popular resort hotel has 300 rooms and is usually fully booked. About 4% of the time a reservation is canceled before 6:00 p.m. deadline with no penalty. What is the probability that at least 280 rooms will be occupied? Use binomial distribution to find the exact value and the normal approxi

    		•
  • Q : Probability and Statistics

    Instructions: Do your work on this question and answer sheet. Please print or write legibly, and, as always, be complete but succinct. Record your answer and your supporting work in the designated space. Explain your method of solution and be sure to label clearly any

    		•
  • Q : MANOVA and Reflection Activity 10:

    Activity 10: MANOVA and Reflection 4Comparison of Multiple Outcome Variables This activity introduces you to a very common technique - MANOVA. MANOVA is simply an extension of an ANOVA and allows for the comparison of multiple outcome variables (again, a very common situation in research a

    		•
  • Q : What is your statistical decision

    Question 1 Do parents with more children travel more than parents of small families? To find out, a survey was done of a large number of adults. Respondents were asked how many children they had and how many times

    		•
  • Q : Probability of winning game Monte Carlo

    Monte Carlo Simulation for Determining Probabilities 1. Determining the probability of winning at the game of craps is difficult to solve analytically. We will assume you are playing the `Pass Line.'  So here is how the game is played: The shooter rolls a pair of

    		•
  • Q : Correlation Define the term Correlation

    Define the term Correlation and describe Correlation formula in brief.

    		•
  • Q : Problem related to playing cards Cards

    Cards are randomly drawn one at the time and with replacement from a standard deck of 52 playing cards. (a) Find the probability of getting the fourth spades on the 10th draw. (b) Determine the

    		•
  • Q : Grouped Frequency Distributions Grouped

    Grouped Frequency Distributions: Guidelines for classes: A) There must be between 5 to 20 classes. B) The class width must be an odd number. This will assure that the class mid-points are integers rather than decimals. C) The classes should be mutually exclusive. This signifies that no data valu

    		•
  • Q : Find the cumulative distribution

    You must use the pre-formatted cover sheet when you hand in the assignment. Out full detailed solutions. Sloppy work will naturally receive a lower score. 1. Suppose at each step, a particle moving on sites labelled by integer has three choices: move one site to the right with pro

    		•
  • Q : Null hypothesis In testing the null

    In testing the null hypothesis H0: P=0.6 vs the alternative H1 : P < 0.6 for a binomial model b(n,p), the rejection region of a test has the structure X ≤ c, where X is the number of successes in n trials. For each of the following tests, d

    		•