ELet X Exponential(0). Find P(IX — px I > kax) for k > 1. Compare this to the bound you get from Chebyshev's inequality. ¦ Let X N Poisson(A). Use Chebyshev's inequality to show that IP(X > 2A) e)...

ELet X Exponential(0). Find P(IX — px I > kax) for k > 1. Compare this to the bound you get from Chebyshev's inequality. ¦ Let X N Poisson(A). Use Chebyshev's inequality to show that IP(X > 2A) < 1/a.="" ¦="" let="" xj.,="" ,="" xn="" ti="" bernoulli(p)="" and="" xn="n-1" e7_,="" xi.="" bound="" p(itcn="" —="" pi=""> e) using Chebyshev's inequality and using Hoeffding's inequality. Show that, when n is large, the bound from Hoeffding's inequality is smaller than the bound from Chebyshev's inequality. ? Let Z N N(0,1). Find P(IZI > t) and plot this as a function of t. From Markov's inequality, we have the bound IP(IZI > t) 0. Plot these bounds for k = 1, 2,3,4,5 and compare them to the true value of P(IZI > t). Also, plot the bound from Mill's inequality. ¦Let X1, , Xn ti N(0,1). Bound P(IXn > t) using Mill's inequality, where Xn = n-1 Ein 1 Xi. Compare to the Chebyshev bound.