Continuous Random Variables

These are really helpful, thank you.

Thank you for these, really clear solutions, very helpful! In case you hadn't spotted, on the second ppt I think there is a typo - the garage example pdf should be 12 rather than 120 otherwise the pdf doesn't integrate to 1 so isn't valid. Following on from this E(X) is not 6 (which surely it can't be as X is only defined between 0-1?) but fixing the pdf to 12 gives an expected value of 0.6 (600litres) which would seem to sort that out.