Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Approximating Standard Errors

  1. Feb 5, 2010 #1
    Hi, I have a question about standard errors in the context of this problem. Any help would be greatly appreciated:

    Suppose X is a discrete random variable with

    P(X=0) = 2y/3
    P(X=1) = y/3
    P(X=2) = 2(1-y)/3
    P(X=3) = (1-y)/3

    Where 0<=y<=1. The following 10 independent observations were taken from such a distribution: (3,0,2,1,3,2,1,0,2,1).

    Find the method of moments estimate of y, an approximate standard error for your estimate, the MLE of y, and an approximate standard error of the MLE.

    I have found the method of moments estimate of y (5/12) and the MLE (.5) but I'm not sure how to go about approximating the standard errors. What I initially did for the SE of the first estimate was to calculate the different y's based on the observed probabilities of the X's, then add the squared differences between them and 5/12, divide by 4, and take the squared root, but that doesn't seem quite right. Sorry to ask such an elementary question, but I'm really puzzled as to how to do this. Thanks in advance!
  2. jcsd
  3. Feb 5, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    What you are missing is an adjustment for the sample size.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook