--%>
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 : Non-parametric test what is the

    what is the appropriate non-parametric counterpart for the independent sample t test?

    		•
  • 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 : Describe what happens to the confidence

     A nurse practitioner working in a dermatology clinic is studying the efficacy of tretinoin in treating women's post partum abdominal stretch marks.  From a sample of 15 women, the mean reduction of stretch mark score is -0.33 with a sample standard deviation of 2.46.  Describe wha

    		•
  • 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 : Probability problem A) What is the

    A) What is the probability of getting the following sequence with a fair die (as in dice):B) What is the probability of getting the same sequence with a die that is biased in the following way: p(1)=p(2)=p(3)=p(4)=15%;

    		•
  • Q : Probability on expected number of days

    It doesn't rain often in Tucson. Yet, when it does, I want to be prepared. I have 2 umbrellas at home and 1 umbrella in my office. Before I leave my house, I check if it is raining. If it is, I take one of the umbrellas with me to work, where I would leave it. When I

    		•
  • Q : Calculate confidence interval A nurse

    A nurse anesthetist was experimenting with the use of nitronox as an anesthetic in the treatment of children's fractures of the arm.  She treated 50 children and found that the mean treatment time (in minutes) was 26.26 minutes with a sample standard deviation of

    		•
  • Q : Binomial distribution 1) A Discrete

    1) A Discrete random variable can be described as Binomial distribution if is satisfies four conditions, Briefly discuss each of these conditions2) A student does not study for a multiple choice examination and decides to guess the correct answers, If the

    		•
  • 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 : How you would use randomization in

    The design of instrument controls affects how easily people can use them. An investigator used 25 students who were right-handed to determine whether right-handed subjects preferred right-handed threaded knobs. He had two machines that differed only in that one had a

    		•