Sampling Distribution for a Selection from a Discrete Distribution

In the UK coins come as 1p,2p, 5p, 10p, 20p, 50p, £1 or £2 coins. Suppose you have 5 1p coins,3 2p coins and 2 5p coins. You select three coins and are onlyinterested in the total value of the selection. To find the samplingdistribution X for the value of the selction, we must list all thepossible values of the selection, along with the probability of eachone.

Selection/p

Value/p X

Probability, P(X=x)

1, 1, 1

3

1, 1, 2 or 1, 2, 1 or 2, 1, 1

4

1, 2, 2 or 2, 1, 2 or 2, 2, 1

5

2, 2, 2

6

1, 1, 5 or 1, 5, 1 or 5, 1, 1

7

1, 2, 5 or 1, 5, 2 or 2, 1, 5 or 2, 5, 1 or 5, 1, 2or 5, 2, 1

8

2, 2, 5 or 2, 5, 2 or 5, 2, 2

9

1, 5, 5 or 5, 1, 5 or 5, 5, 1

11

2, 5, 5 or 5, 2, 5 or 5, 5, 2

12

We can find the expectedvalue of the selection using the formula

andthe variance is

The variance is then

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