Question

A random variable x follows the continuous uniform distribution with a lower bound of -6 and an upper bound of 16. What is the probability density function (PDF) of x?

Answer 1

The probability density function (PDF) for a continuous uniform distribution with a lower bound of -6 and an upper bound of 16 is f(x) = 1/22 for -6 ≤ x ≤ 16.

Step-by-step explanation:

The probability density function (PDF) for a continuous uniform distribution where a random variable x has a lower bound of -6 and an upper bound of 16 is given by the formula f(x) = ⅛ / (b - a) for a ≤ x ≤ b. Since this is a uniform distribution, the PDF is constant over the interval from a to b. In this case, a = -6 and b = 16, so the length of the interval is 16 - (-6) = 22. Therefore, the PDF is f(x) = 1 / 22 for -6 ≤ x ≤ 16.

The probability that the random variable equals any single value is 0. This is because for continuous distributions, we are interested in the probability over an interval rather than a single point. The entire area under the PDF curve equals 1, which corresponds to the total probability for all outcomes within the domain of x.