Question

Suppose X is a random variable with p(X 0) 4/5, p(X-1) 1/10, p(X-9) 1/10. Then (a) Compute Var [X] and B [X] (b) What is the upper bound on the probability that X is at least 20 obained by applying Markov's inequality? c) What is the upper bound on the probability that X is at least 20 obained by applying Chebychev's inequality'?

Please show your work with a brief but logical explanation.

Answer 1

har Given a 1 0 9 ax E(X) I o N o W E(x) 2 4 1 0 5

& 2 82 1 0 Ex) - ETIx) 2 72 bBy Markav's inequality, we is a know hat nan do nへ non-negative Vam able with ,ao n is problem x is also non-neg-a h ve nan dow vamable asPX o) a least- 20 2.0

The uppe bound is 0 0S By Chebu s hevs inequal we know hat if X is a wirh. Van iable Y'an dovn 2 7 2 o v 2 2 If we put t 19, we geh

(19) 0 V 0 , So . The upper bound is 0 02