Given that F is a distribution function then it is going to be said to be non decreasing.
<h3>How to define the random variable</h3>
Let Y = F(x)
Then we have a distribution function that we can define to be
Gy(Y) = P(Y≤y) = P[F(X)≤y]
= P[x≤F⁻¹(y)]
The inverse is said to exist given that the value F is non decreasing and it is also said to be continuous.
Such that Gy(Y) = F[F⁻¹(y)]
then we have to see f to be the distribution of x
Gy(Y) = y
The PDF of Y is denoted as Y = F(X)
then we would have
d/dy [Gy(Y)] = 1
Given that F is a df, then the value of the distribution function would always be 0, 1.
gy(y) would then have to be 1
0 ≤ y ≤ 1
This tells us that F(X) is a uniform variate of 0,1.
Read more on cumulative distribution function here:
brainly.com/question/14100876
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