## Probability question involving generating functions and expectation

Hi,

I'm stuck on the very last part of 5.b

https://www.maths.ox.ac.uk/system/fi...PaperC2003.pdf

I can't prove the inequality, would it be right to say the expected premium would be
£M(lambda)^(E[Y]-1)

Then I get (lambda)^(E[Y]-1)>k.. thinking I must have done something wrong because can't see how to get this to the one stated.