Question

The probability of generating a random number equal to any fixed point under a continuous uniform distribution:

a) Is 0
b) Is 1
c) Is dependent on the distribution range
d) Is 0.5

Answer 1

The probability of selecting any single point in a continuous uniform distribution is 0 because probabilities for continuous variables are defined over intervals, not specific points.

Step-by-step explanation:

The question deals with the concept of probability in a continuous uniform distribution. In such a distribution, the probability of selecting any single point, let's say P(x = c), is always 0. This is because for a continuous random variable, probabilities are calculated over a range of values, not for exact values. If you are trying to find the probability in a range, for instance, P(c < x < d), you calculate the area under the probability density function (PDF) that lies between the two points c and d.

In the specific example of the uniform distribution, the PDF is represented as a rectangle, which makes it relatively straightforward to calculate the probabilities as areas under the curve. For a given interval on a uniform distribution, you would find the area by simply computing the width of the interval (d - c) multiplied by the height of the PDF