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) = ?

1

Step-by-step 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

d

step-by-step explanation:

22.83 repeating

step-by-step explanation:

137 ÷ 6 is 22.8333333 therefore we understand that 3 is repeating.

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