Show work, need it to study 0.95?Note:In practice, the bound provided by Chebyshev's inequality is usually very "loose",in the sense that n actually only needs to be much smaller for P(0.5 0.95...

Show work, need it to study
0.95 to hold. A tighter bound for the setting we considered can be obtained by Hoeffding's inequality (Example 6.15 in Wasserman) or Central Limit Theorem (we will study this in class). Note that the bounds from Chebyshev's inequality or Hoeffding's inequality are finite sample in that they hold for any finite n. On the contrary, the bound from Central Limit Theorem is asymptotic, in that it is a statement about n → x, and it only holds approximately for finite n. "/>
Extracted text: Consider flipping a (biased) coin for which the probability of head is p. The fraction of heads after n independent tosses is Xn. Law of large numbers imply that Xn → p as n → 0. This P does not mean that X, will exactly equal to p, but rather the distribution of X, is tightly concentrated around for large n. Suppose 0.1 < p="">< 0.9.="" use="" chebyshev's="" inequality="" to="" obtain="" a="" lower="" bound="" on="" р(p="" -="" 0.1="">< х,=""><р+0.1). suppose="" p="0.6." using="" the="" above="" lower="" bound="" derived="" using="" chebyshev's="" inequality,="" how="" large="" should="" n="" be="" so="" that="" p(0.5="">< xn="">< 0.7)=""> 0.95? Note: In practice, the bound provided by Chebyshev's inequality is usually very "loose", in the sense that n actually only needs to be much smaller for P(0.5 < x,="">< 0.7)=""> 0.95 to hold. A tighter bound for the setting we considered can be obtained by Hoeffding's inequality (Example 6.15 in Wasserman) or Central Limit Theorem (we will study this in class). Note that the bounds from Chebyshev's inequality or Hoeffding's inequality are finite sample in that they hold for any finite n. On the contrary, the bound from Central Limit Theorem is asymptotic, in that it is a statement about n → x, and it only holds approximately for finite n.