- #1

- 5

- 0

Suppose that X = Y + Z, where Y is the integral part of X and Z is the fractional part of X:

Y = IP(X), Z = FP(X).

Which is the following conditional probability:

P(Z < z | Y = n) for 0 ≤ z < 1 and n = 0, 1, … ?

- Thread starter Postante
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- #1

- 5

- 0

Suppose that X = Y + Z, where Y is the integral part of X and Z is the fractional part of X:

Y = IP(X), Z = FP(X).

Which is the following conditional probability:

P(Z < z | Y = n) for 0 ≤ z < 1 and n = 0, 1, … ?

- #2

- 35,142

- 6,275

P(Z < z | Y = n) = P(X < n+z | Y = n) = P(X < n+z | n <= X < n+1)

Suppose that X = Y + Z, where Y is the integral part of X and Z is the fractional part of X:

Y = IP(X), Z = FP(X).

Which is the following conditional probability:

P(Z < z | Y = n) for 0 ≤ z < 1 and n = 0, 1, … ?

= (F(n+z)-F(n))/(F(n+1) - F(n))

= (e

= (1-e

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