Question

Let U be a random variable uniformly distributed on

(0,1). Determine the probability density function of Y=1−U.

a) f(y)=1
b) f(y)=0.5
c) f(y)=2
d) f(y)=1−y

Answer 1

To determine the pdf of Y=1−U, where U is uniformly distributed on (0,1), we find the derivative of the cdf of Y.

Step-by-step explanation:

In this case, we have Y = 1 - U, where U is a random variable uniformly distributed on the interval (0,1). To determine the probability density function (pdf) of Y, we need to find the derivative of the cumulative distribution function (cdf) of Y.

Since Y = 1 - U, the cdf of Y is given by F(y) = P(Y ≤ y) = P(1 - U ≤ y) = P(U ≥ 1-y) = 1 - P(U < 1-y) = 1 - (1-y), for 0 ≤ y ≤ 1.

Taking the derivative of the cdf, we get the pdf of Y as f(y) = dF(y)/dy = d(1 - (1-y))/dy = 1, for 0 ≤ y ≤ 1.