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CT3 IFoA September 2011 - Question 8

T

trackr

Member
Hi guys,

This is a pretty straight forward question...but with regards to part (ii) where they ask to calculate exact probability I got this:

(for simplicity I have used 10*Lambda = x)

P(2<= X <=3) = P(X<=3) - P(X<=2)

However by the looks of the solution, they have used:

P(X<=3) - P(X<=1).

I am not sure why they used P(X<=1) when it clearly states in the question it is P(0.2<=lambda<=0.3)

Can someone please clarify?

Thanks in advance!
 
Hopefully this response is correct. Think about it this way - for a discrete random variable X,
P(2<=X <=3) = P(X=2) + P(X=3) [1]

What you've written is P(2<= X <=3) = P(X<=3) - P(X<=2), so let's dissect the right hand side like I have done above.
First of all, P(X<=3) = P(X=1) + P(X=2) + P(X=3).
And for the 2nd term, P(X<=2) = P(X=1) + P(X=2).

Hence P(X<=3)-P(X<=2) = P(X=3) [2]

As you can see, Eqn [1] is different to Eqn [2].
If you do the same analysis with "P(X<=3) - P(X<=1)." (which is from the solution) you should find that you get the same as Eqn[1] which is the correct one.
 
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