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March 25th, 2009, 06:45 PM
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| |  Chi Square random variables
Q:
if X and Y are independent chi-square random variables with 3 and 6 degrees of freedom, respectively, determine the probability that X + Y will exceed ten. (Use the tables at the back of the text).
Im not sure how to go about this problem, because the back of the book has nothing of 2 chi-squares added together.
Should i find P(χ²₉ > 10) ? that is a chi-square with 3 + 6 degrees of freedom? |
March 26th, 2009, 03:44 PM
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that is the probability that a chi-square w 9 degrees of freedom exceeds 10.
The integration is nasty but you can get a nice answer via an online calculator... http://www.danielsoper.com/statcalc/
in particular... http://www.danielsoper.com/statcalc/calc11.aspx
plug in 10 and 9 and I get... Probability (One-Tailed): 0.350485
which makes sense since the mean is 9.
My guess was .4 to .45.
Last edited by matheagle; March 26th, 2009 at 05:53 PM.
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March 26th, 2009, 05:31 PM
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Quote:
Originally Posted by jjs2168  Q:
if X and Y are independent chi-square random variables with 3 and 6 degrees of freedom, respectively, determine the probability that X + Y will exceed ten. (Use the tables at the back of the text).
Im not sure how to go about this problem, because the back of the book has nothing of 2 chi-squares added together.
Should i find P(χ²₉ > 10) ? that is a chi-square with 3 + 6 degrees of freedom? | You can use a moment generating function approach to prove that the sum of two independent chi-square random variables of degrees of freedom  and  has a chi-square distribution with  degrees of freedom.
__________________ There are two things you should never try to prove: the impossible and the obvious. The greater danger for most of us lies not in setting our aim too high and falling short; but in setting our aim too low and achieving our mark. (Michelangelo Buonarroti)
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