Question

Let X be a binomial distribution with parameters n and p, and k a number such that $p < k < 1$. 1. Find an upper bound for $P(X ge kn)$ using Markov's inequality. 2. Find an upper bound for $P(X ge kn)$ using Chebyshev's inequality. 3. Let $p = frac{1}{2}$ and $k = frac{3}{4}$. Which inequality gives the tighter bound?

          Let X be a binomial distribution with parameters n and p, and k a number such that $p < k < 1$.
1. Find an upper bound for $P(X ge kn)$ using Markov's inequality.
2. Find an upper bound for $P(X ge kn)$ using Chebyshev's inequality.
3. Let $p = frac{1}{2}$ and $k = frac{3}{4}$. Which inequality gives the tighter bound?

$Let X be a binomial distribution with parameters n and p, and k a number such that p < k < 1. 1. Find an upper bound for P(X ge kn) using Markov's inequality. 2. Find an upper bound for P(X ge kn) using Chebyshev's inequality. 3. Let p = frac12 and k = frac34. Which inequality gives the tighter bound?$

Added by Jessica P.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Akhil Choudhary

04/15/2022

Step 1

Step 1: Using Markov's inequality, we found that $ P(X > kn) < \frac{P}{k} $ where $ P = 2 $ and $ k = \frac{3}{4} $. Show more…

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Let X be a binomial distribution with parameters n and p, and k a number such that p < k < 1. 1. Find an upper bound for P(X >= kn) using Markov's inequality. 2. Find an upper bound for P(X >= kn) using Chebyshev's inequality. 3. Let p = 1/2 and k = 3/4. Which inequality gives the tighter bound?