In this problem we look at two general 'random inequalities'. You can use the distribution maker interactivity to create distributions to try to solve the two parts of the problem.

Part 1
Markov's inequality tells us that the probability that the modulus of a random variable X exceeds any random positive number a is given by a universal inequality as follows:

P(|X| > a) £ E(X)
a??
In this expression the exponent of the denominator on the right hand side is missing, although Markov showed that it is the same whole number for every possible distribution . Given this fact, experiment with the various distributions to find the missing value (??).

Part 2
Another important general statistical result is Chebyshev's inequality , which says that

P(|X-m| ³ ks) £ 1
k2
where m and s are the mean and standard devitation of the distribution X respectively. This is true for any distribution and any positive number k. Can you make a probability distribution for which the inequality is exactly met when k=2? In other words, use the distribution maker to create a distribution X for which
P(|X-m| ³ 2s)= 1
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