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.
