Question

Let F be a continuous distribution function. If U is uniformly distributed:

a) F(U)
b) U²
c) 1−F(U)
d) 1/2 F(U)

Answer 1

In a continuous distribution function, F(U) represents the cumulative distribution function (CDF), U² represents the probability density function (PDF), 1−F(U) represents the probability of the random variable being greater than U, and 1/2 F(U) does not have a specific meaning or interpretation.

Step-by-step explanation:

In a continuous distribution function, the random variable U is uniformly distributed between 0 and 1. Let F be the continuous distribution function.

a) F(U) represents the cumulative distribution function (CDF), which gives the probability that the random variable is less than or equal to U.

b) U² represents the probability density function (PDF) of U, which is a constant value of 1.

c) 1−F(U) represents the probability that the random variable is greater than U.

d) 1/2 F(U) does not have a specific meaning or interpretation in this context.