2. Problem. Let X be a random variable such that E(X)= 0. Assuming that thevariance of X exists, show thatHint: Note thatP(X ≥a) ≤var (X)var (X) + a²for all a > 0.P(X≥a) ≤ P ((X+t)² ≥ (a+t)²)Apply the Markov inequality and optimize on t.for all t20.

Given that X is a random variable such that E(X)=0 and its variance, var(X) exists. We have to show…

Answered: 2. Problem. Let X be a random variable…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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2. Problem. Let X be a random variable such that E(X)= 0. Assuming that the variance of X exists, show that P(X ≥a) ≤ Hint: Note that var(X) var(X) + a² for all a > 0. P(X≥a) ≤ P((X+t)² (a+t)²) for all t≥ 0. Apply the Markov inequality and optimize on t.