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The distribution X and Y with total number of observations 36 and 64, and mean 4 and 3 respectively are combined. What is the mean of the resulting distribution X + Y ?

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According to the question, 

4 = x/36 and 3 = y/64 

⇒ x = 4 × 36 and y = 3 × 64 

⇒ x = 144 and y = 192 

Now, x + y = 144 + 192 = 336 

And total number of observations = 36 + 64 = 100 

Thus, mean = 336/100 = 3.36.

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