Distinguish X1+X2 from 2X

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

Screenshot_2015-05-27-13-52-49

There were two mistakes made:

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

2) Calculation of variance

Here is the correct solution:

hamper

1

2

Smallest possible value of n = 9

————————-

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:

form

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: