By the argument in the last video, if the Xi are i.i.d. with mean μ and variance σ2 , and if Mn=(X1+⋯+Xn)/n , then we have an inequality of the form

Question

P(|Mn−μ|≥ϵ)≤aσ2n,

for a suitable value of a .

a) If ϵ=0.1 , then the value of a is:
unanswered
b) If we change ϵ=0.1 to ϵ=0.1/k , for k≥1 (i.e., if we are interested in k times higher accuracy), how should we change n so that the value of the upper bound does not change from the value calculated in part (a)?

n should

stay the same
increase by a factor of k
increase by a factor of k2
decrease by a factor of k
none of the above

Answer 1

Video?

Answer 2

a). a = 100
b). increase by a factor of k^2