Difference between two normal distributions

Oct 2009
196
2
I have two normal distributions, with different means but the same variance. How can I find the probability for that the difference between a sample taken from each distribution is above x? Not sure how to approach this. Would appreciate any help.
 

matheagle

MHF Hall of Honor
Feb 2009
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\(\displaystyle P(\bar X-\bar Y>a)=P\left( {(\bar X-\bar Y)-(\mu_X-\mu_Y)\over \sqrt{ {\sigma^2\over n} + {\sigma^2\over m}}}>{a-(\mu_X-\mu_Y)\over \sqrt{ {\sigma^2\over n} + {\sigma^2\over m}}}\right)\)

\(\displaystyle =P\left( Z>{a-(\mu_X-\mu_Y)\over \sqrt{ {\sigma^2\over n} + {\sigma^2\over m}}}\right)\)