--%>

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 : True and False Statement Discuss the

    Discuss the following statements and explain why they are true or false: a)      Increasing the number of predictor variables will never decrease the R2 b)      Multicollinearity affects the int

  • Q : Random variables Random variables with

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

  • Q : Conclusion using p-value and critical

    A sample of 9 days over the past six months showed that a clinic treated the following numbers of patients: 24, 26, 21, 17, 16, 23, 27, 18, and 25. If the number of patients seen per day is normally distributed, would an analysis of these sample data provide evid

  • Q : Probability of signaling Quality

    Quality control: when the output of a production process is stable at an acceptable standard, it is said to be "in control?. Suppose that a production process has been in control for some time and that the proportion of defectives has been 0.5. as a means of monitorin

  • Q : Statistics A nurse practitioner working

    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 what happens to the c

  • Q : Frequency Distributions Define the term

    Define the term Frequency Distributions?

  • 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 : 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 : Bayesian Point Estimation What are the

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

  • 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