In a delivery service, the time for a package to be delivered is uniformly distributed between $10$ and $30$ minutes. Find the probability that the delivery time is between $15$ and $25$ minutes.

A customer at a café orders a coffee, and the time it takes for the coffee to be prepared is uniformly distributed between $5$ and $15$ minutes. What is the maximum time, in minutes, within which there is a $90\%$ probability the coffee will be ready?

Which two conditions must a function meet to be considered a valid probability density function (pdf)?

Which reasoning correctly explains why P(X = c) = 0 for a continuous random variable with a well-defined pdf?

A continuous random variable has pdf f(x)=k( x ) on [0,2] where f(x)=ax+b produces a triangular density with f(0)=0 and f(2)=1. Determine P(0.5 ≤ X ≤ 1.5).