B use chebyshevs inequality to find the confi- dence level

Question

X₁,..., X_n are n independent identically distributed samples of random variable X with PMF

(a) How is E[X] related to P_X (1)?

(b) Use Chebyshev's inequality to find the confi- dence level α such that M₉₀(X), the estimate based on 90 observations, is within 0.05 of P_X (1). In other words, find α such that

(c) Use Chebyshev's inequality to find out how many samples n are necessary to have M_n(X) within 0.03 of P_X (1) with confidence level 0.1. In other words, find n such that