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

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6