Since the Q-function represents the tail probability of a Gaussian random variable, we can use the various bounds on tail probabilities to produce bounds on the Q-function.

(a) Use Markov's inequality to produce an upper bound on the Q-function.

Hint: a Gaussian random variable has a two-sided PDF, and Markov's inequality requires the random variable to be one-sided. You will need to work with absolute values to resolve this issue.

(b) Use Chebyshev's inequality to produce an upper bound on the Q-function.