Compute the total variation distance between

A First Course in Probability (10th Edition)
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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
Transcribed Image Text: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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