Question

Let x be a random number between 0 and 1 produced by the idealized uniform random number generator. remember the probability of picking a number between 0 and 0.1 is 0.1 and the probability of picking a number between 0.2 and 0.3 is 0.1. find the following probabilities of the following

Answer 1

In a uniform distribution, the probability of a number falling between two values is equal to the length of the interval between those values.

Step-by-step explanation:

The question revolves around the concept of probability in a uniform random number generator scenario within the interval [0, 1]. To find the probability that a random number x falls between two specific values, you would typically calculate the area under the probability density function (PDF) corresponding to that interval. However, in a uniform distribution, the PDF is constant, meaning the area (and therefore the probability) corresponds simply to the length of the interval on the x-axis.

For example, the probability of x is between 0.2 and 0.3 is the length of the interval [0.2, 0.3], which is 0.1. Therefore, P(0.2 < x < 0.3) = 0.1. Similarly, if we wanted to find the probability that x falls between any two values within [0, 1] when x is uniformly distributed, we'd calculate the length of that interval.