Question

18 (Lamperti) Let X be a non-negative random variable. What is the best upper bound you can give for $P(X \ge a)$ if you know (a) $E(X) = 20$. (b) $E(X) = 20$ and $V(X) = 25$. (c) $E(X) = 20$, $V(X) = 25$, and X is symmetric about its mean.

          18 (Lamperti) Let X be a non-negative random variable. What is the best upper bound you can give for $P(X \ge a)$ if you know
(a) $E(X) = 20$.
(b) $E(X) = 20$ and $V(X) = 25$.
(c) $E(X) = 20$, $V(X) = 25$, and X is symmetric about its mean.

18 (Lamperti) Let X be a non-negative random variable. What is the best upper bound you can give for P(X ≥ a) if you know
(a) E(X) = 20.
(b) E(X) = 20 and V(X) = 25.
(c) E(X) = 20, V(X) = 25, and X is symmetric about its mean.

Added by Isabel S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

07/14/2023

Step 1

Markov's inequality states that for a non-negative random variable X and a positive number a, $$P(X \ge a) \le \frac{E(X)}{a}$$ Show more…

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18 (Lamperti) Let X be a non-negative random variable. What is the best upper bound you can give for P(X≥ a) if you know (a) E(X) = 20. (b) E(X) = 20 and V(X) = 25. (c) E(X) = 20, V(X) = 25, and X is symmetric about its mean.