Probability question involving generating functions and expectation

[LHS]

Homework Statement

Hi,

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

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

Homework Equations

The Attempt at a Solution

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.

 

[Stephen Tashi]

I can't get to that PDF. By the way, if you decide to use LaTex on this forum, after you preview your post, tell your browser to reload the page. There is a bug in the forum software that usually makes the initial previews look screwy.