## Distinguish X1+X2 from 2X

This challenging question on normal distribution was posted in Edusnap by a student.

1) Interpreting the distribution of 2 large hampers and n small hampers as 2L + nS.

2) Calculation of variance

Here is the correct solution:

Smallest possible value of n = 9

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When the question mentions n items, the distribution is X1+X2+…Xn.  When the question asks for “n times of a randomly chosen..”, then the distribution is nX.

Students also need to be familiar with calculating the expectation and variance of the sum or difference of normal distribution using the formula: