--%>
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 : 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 : 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 : 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 : Problem on layout A manufacturing

    A manufacturing facility consists of five departments, 1, 2, 3, 4, and 5. It produces four components having manufacturing product routings and production volumes indicated below.   1. Generate the from-to matrix and the interaction matrix. Use a

    		•
  • 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 : Variation what are the advantages and

    what are the advantages and disadvantages of seasonal variation

    		•
  • Q : Bayesian Point Estimation What are the

    What are the Bayesian Point of estimation and what are the process of inference in Bayesian statistics?

    		•
  • Q : Pearsons correlation coefficient The

    The table below illustrates the relationship between two variable X and Y. A

    		•
  • Q : Use the law of iterated expectation to

    Suppose we have a stick of length L. We break it once at some point X _

    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

    		•