--%>
Assignment Help - homework help

Random variables

Random variables with zero correlation are not necessarily independent. Give a simple example.

 

 

E

Expert

Verified

Let X be a normally-distributed random variable with

  Mean zero.  Let Y = X^2.  Obviously, X and Y are not independent: knowing X, gives the value of Y.

  The covariance of X and Y is  Cov(X,Y) = E(XY) - E(X)E(Y) = E(X^3) - 0*E(Y) = E(X^3)              = 0,

  because the distribution of X is symmetric around zero.  correlation r(X,Y) = Cov(X,Y)/Sqrt[Var(X)Var(Y)] = 0,   the random  variables are not independent, but correlation is zero.

   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 : 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 : 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 : 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 : 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 : 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 : 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 : 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 : 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 : Discrete and continuous data

    Distinguish between discrete and continuous data in brief.

    		•