January 2008 - Question 4



First, we need to work out the expectation. Lets look at the formula...

E(X) = ΣrP(X=r)

This means that we need to times each number top row by the one below it and add them all together...

1 × 0.2 + 2 × 0.16 + 3 × 0.128 + 4 × 0.512 = 2.952


Now we need to work out the variance...

Var(X) = Σr2P(X=r) - E(X)2


Σr2P(X=r) means that we need to square each r value before multiplying it by the P(X=r) value and finding the sum of them.

1 × 0.2 + 4 × 0.16 + 9 × 0.128 + 16 × 0.512 = 10.184


And then we need to square E(X)...

2.9522 = 8.714304


Now we just need to take the E(X)2 from the ΣrP(X=r).

10.184 - 8.714304 = 1.47 (2 d.p.)





As it's the expected cost, all we have to do is multiply the £45,000 by E(X).

45,000 × 2.952 = £132,840




Even though this sounds complicated, it's pretty simple. We just need to put the original table into graph form.
As it's two marks, remember to label the axis correctly and to give the right height of lines.

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