--%>
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 : Problem on Poisson distribution The

    The number of trucks coming to a certain warehouse each day follows the Poisson distribution with λ= 8. The warehouse can handle a maximum of 12 trucks a day. What is the probability that on a given day one or more trucks have to be sent away? Round the answer

    		•
  • 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 corresponding t value or s

    1)    Construct a 99% confidence interval for the population mean µ.   2)    At what significance level do the data provide good evidence that the average body temperature is

    		•
  • Q : Non-parametric test what is the

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

    		•
  • 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 : Analytical Report Hi I WOULD LIKE TO

    Hi I WOULD LIKE TO KNOW IF YOU CAN HELP ME TO DO THE ASSIGNMENT IN HEALTH STATISTICS THANKS

    		•
  • Q : Error probability As of last year, only

    As of last year, only 20% of the employees in an organization used public transportation to commute to and from work. To determine if a recent campaign encouraging the use of public transportation has been effective, a random sample of 25 employees is to be interviewe

    		•
  • Q : Statistics Homework with SAS File is

    File is attached, need it by 8:30 AM Pacific (Seattle, WA) time. No delay acceptable. Need it March 25, 2014 on 8:30 AM Pacific time.

    		•
  • 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

    		•
  • 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

    		•