# Markov and Chebyshev Inequalities

1. Aug 24, 2009

### WHB3

1. The problem statement, all variables and given/known data

Let X be a random variable; show that for a>1 and t>0,
P(X>=(1/t)(ln(a)))<=(1/a)(Mx(t))

2. Relevant equations

3. The attempt at a solution

I know, from a previous problem, that, where X is a random variable and K is a constant,
P(X>t)<=E(exp(kX))/(exp(kt))

For the right side of the equation of the problem, I know that Mx(t)=E(exp(tx)), which is the numerator of the equation, but I don't know how to show that the denominator ="a".

Any helpful hints would be very much appreciated.