Combining normal distributions

S

szakyl

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Jan 31, 2020
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The situation I have is that there are 2 independent samples. Sample 1 has a mean of 10 and a standard deviation of 1. Sample 2 has a mean of 9 and a standard deviation of 2. A value is taken from each sample. Finally, the larger of these 2 values is selected. I would like to determine the mean of this final value. Running the situation numerous times in Excel, I've determined the mean to be 10.5 (approximately). Is there a mathematical formula to determine the exact answer? I've tried Googling this, but haven't been able to come up with a good search.
 
#1 A "value" doesn't have a mean.
#2 Is your question, What is the mean value of the distribution max(X1,X2) where X1 is the random variable of your (10,1) distribution and X2 is the random variable of your (9,2) distribution?
#3 Why not find the Standard Deviation as well?
#4 Is either distribution particularly Normal?
 
#1 and 2 - I apologize for the lack of correct terminology and phrasing. I never had a formal stats course.
“What is the mean value of the distribution max(X1,X2) where X1 is the random variable of your (10,1) distribution and X2 is the random variable of your (9,2) distribution?” is what I am looking for.
#3 - I thought I’d be more likely to get a response if I didn’t ask multiple questions within the same post, but I would like the standard deviation as well.
#4 - Yes, the samples are normally distributed.
 
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