Question

How to use Chebyshev bound to achieve this question ? Let X be a Geometric random...

How to use Chebyshev bound to achieve this question ?

Let X be a Geometric random variable, with success probability p.
1) Use the Markov bound to find an upper bound for P (X ≥ a), for a positive integer a.
2) If p = 0.1, use the Chebyshev bound to find an upper bound for P(X ≤ 1). Compare it with the
actual value of P (X ≤ 1) which you can calculate using the PMF of Geometric random variables; what do you observe?

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let Y denote a geometric random variable with probability of success p, (a) Show that for...
Let Y denote a geometric random variable with probability of success p, (a) Show that for a positive integer a, P(Y > a) = (1 − p) a (b) Show that for positive integers a and b, P(Y > a + b|Y > a) = P(Y > b) = (1 − p) b This is known as the memoryless property of the geometric distribution.
let x be a discrete random variable with positive integer outputs. show that P(x=k) = P(...
let x be a discrete random variable with positive integer outputs. show that P(x=k) = P( x> k-1)- P( X>k) for any positive integer k. assume that for all k>=1 we have P(x>k)=q^k. use (a) to show that x is a geometric random variable.
(14pts) Let X and Y be i.i.d. geometric random variables with parameter (probability of success) p,...
(14pts) Let X and Y be i.i.d. geometric random variables with parameter (probability of success) p, 0 < p < 1. (a) (6pts) Find P(X > Y ). (b) (8pts) Find P(X + Y = n) and P(X = k∣X + Y = n), for n = 2, 3, ..., and k = 1, 2, ..., n − 1.
Let X be a discrete random variable with positive integer outputs a show that p (X=...
Let X be a discrete random variable with positive integer outputs a show that p (X= K)= P( X> K-1) - P( X> k) for any positive integer k b Assume that for all k >I we have P (X>k)=q^k  use l() to show that X is a geometric random variable
Let X~Poisson(4) random variable and Y an independent Bin(10,1/2) random variable. (a) Use Markov's inequality to...
Let X~Poisson(4) random variable and Y an independent Bin(10,1/2) random variable. (a) Use Markov's inequality to find an upper bound for P(X+Y > 15). (b) Use Chebyshev's inequality to find an upper bound for P(X+Y > 15)
Given that X is a geometric random variable with success probability = 1/3, Find Pr(X<1003 |...
Given that X is a geometric random variable with success probability = 1/3, Find Pr(X<1003 | X>1000). (Hint: must use memory-less property of geometric random variables).
Let X~Geometric(1/3) and let Y=|X-5|. Find the range and PMF of Y. Starting with the equation...
Let X~Geometric(1/3) and let Y=|X-5|. Find the range and PMF of Y. Starting with the equation Px(X=k) = (1-p)^k-1 * p
Let X and Y be independent Geometric(p) random variables. What is P(X<Y)?
Let X and Y be independent Geometric(p) random variables. What is P(X<Y)?
A. (i) Consider the random variable X with pmf: pX (−1) = pX (1) = 1/8,...
A. (i) Consider the random variable X with pmf: pX (−1) = pX (1) = 1/8, pX (0) = 3/4. Show that the Chebyshev inequality P (|X − μ| ≥ 2σ) ≤ 1/4 is actually an equation for this random variable. (ii) Find the pmf of a different random variable Y that also takes the values {−1, 0, 1} for which the Chebyshev inequality P (|X − μ| ≥ 3σ) ≤ 1/9 is actually an equation.
Let X be a geometric random variable with parameter p . Find the probability that X≥10...
Let X be a geometric random variable with parameter p . Find the probability that X≥10 . Express your answer in terms of p using standard notation (click on the “STANDARD NOTATION" button below.)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT