Exercise: Sample mean bounds
2 points possible (graded)
By the argument in the last video, if the Xi are i.i.d. with mean and variance sigma² , and if Mn=(X1+ ....+Xn)/n , then we have an inequality of the form
P(IMn-muI>=a.sigma²/n
for a suitable value of a .
a) If E=0.1, then the value of a is:
unanswered
b) If we change to E=0.1/k, fork>=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
unanswered