Using Chebyshevs inequality, find an upper bound on:
Using Chebyshevs inequality, find an upper bound on: にsum.NG X, in にsum.NG X, in
1. a) Let X ∼ Exponential(λ). Using Markov’s inequality find an upper bound for P(X ≥ a), where a > 0. Compare the upper bound with the actual value of P(X ≥ a). b) Let X ∼ Exponential(λ). Using Chebyshev’s inequality find an upper bound for P(|X − EX| ≥ b), where b > 0.
Let X ~ Geomeric(p). Using Chebyshev's inequality find an upper bound for P(|X – E[X]] >b).
6. If E(x) 16 and E(X?) -292, use Chebyshev's inequality to determine a) A lower bound for P(8< X < 24). (b) An upper bound for P(X 162 18)
Apply Chebyshevs Inequality to lower bound P(O< X < 4) when E(X) 2 and E(X2)-5
Modify X and apply Markov's inequality to upper bound P(X > 3) when X > 2 and E[X] = 2.5.
how do I find the upper bound and lower bound of f(x)=x^4-9x^2+4x+12
Please show your work with a brief but logical explanation. 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'? Suppose X is a random variable with p(X...
Determine an upper bound on the error in using e* ~1+x to approximate e
Problem 2 Prove the following bound known as the Chemoff bound: Let X be a random variable with moment generating function X (s) defined for s > 0, Then for any a and any s > 0, Hint: To prove the bound apply Markov's inequality with X replaced by e) Apply the се Chemoff bound in case X is a standard normal random variable and a > 0. Find the value of s >0 that gives the sharpest bound, i.e,...
2. Suppose that is an exponential random variable with pdf f(y)= e), y>0. a. Use Chebyshev's Inequality to get an upper bound for the probability that takes on a value more than two standard deviations away from the mean. b. Use the given pdf to compute the exact probability that takes on a value more than two standard deviations away from the mean.