Question

Defined the total variation distance to be a distance TV(P,Q) between two probability measures P and Q. However, we will also refer to the total variation distance between two random variables or between two pdfs or two pmfs, as in the following.

Compute TV(X,X+a) for any a∈(0,1), where X∼Ber(0.5).

TV(X,X+a) = ?

Answer 1

1

Explanation:

Computing Tv(X, X + a ) for any a∈(0,1)

Given that : X∼Ber(0.5)

∴ The probability mass function

P(X = 1 ) = 0.5

P(X = 0) = ( 1 - 0.5 )

and expectation E[X] = 0.5

hence ; TV ( X, X + a ) = 1