Compute the total variation distance betweenP = Ber (p)and Q = Ber (g), where p, q € [0, 1] .(If applicable, enter abs(x) for |æ|.)TV (P, Q) =Let X1....,X, be n i.i.d. Bernoulli random variables with some parameter p e [0,1], and X, be their empirical average. Consider the totalvariation distance TV (Ber (X,), Ber (p))between Ber (X) and Ber (p) as a function of the random variable Xm, and hence a random variable itself.Does TV (Ber (X), Ber (p)) necessarily converge in probability to a constant? If yes, enter the constant below; if not; enter DNE.(P)TV (Ber (X,), Ber (p))n00STANDARD NOTATION

Introduction: The probability mass function (p.m.f) of Bernoulli distribution is as given below:

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Compute the total variation distance between

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

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ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

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Question

Compute the total variation distance between
P = Ber (p)
and Q = Ber (g), where p, q € [0, 1] .
(If applicable, enter abs(x) for |æ|.)
TV (P, Q) =
Let X1....,X, be n i.i.d. Bernoulli random variables with some parameter p e [0,1], and X, be their empirical average. Consider the total
variation distance TV (Ber (X,), Ber (p))between Ber (X) and Ber (p) as a function of the random variable Xm, and hence a random variable itself.
Does TV (Ber (X), Ber (p)) necessarily converge in probability to a constant? If yes, enter the constant below; if not; enter DNE.
(P)
TV (Ber (X,), Ber (p))
n00
STANDARD NOTATION

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