Question

A random number between zero and one is generated according to a continuous uniform distribution. What is the probability that the first. Ple number generated will have a value of exactly 0.30?
I know the answer is 0 but I do not clear that, please explain in detail

Answer 1

This is a uniform distribution with

a = 0 B=1

Since we know that
The probability density function of a uniform distribution is

85150.97* = (x)}

This implies that
Cumulative density function of a uniform distribution is

F(x) = 21 - a B-a

P(X = 0.3) = ?
For a continuous, the probability is the integration of probability density function in a given interval. Since if we give a particular point as an interval the integration comes out as 0. Or we can say that the probability for an event in a continuous distribution function(like uniform distribution) can be calculated by finding the area under the distribution curve for that interval. Since a particular point have no area under the curve, Probability at a particular point is equal to 0
P(X = 0.3) = 0