Question

Two girls want to meet at a specified place between 4 and 5 p.m. Let T denote the random variable describing the waiting time of the girl who arrived first. Find the distribution of the random variable T

Answer 1

The distribution of the random variable T is a discrete uniform distribution, where each interval has a probability of 0.01.

Step-by-step explanation:

To find the distribution of the random variable T, we can use the given information that the waiting time for the bus is uniformly distributed from 0 to 75 minutes. Since there are 100 riders randomly sampled, we can divide the waiting time into 100 equal intervals, each representing the waiting time for one rider. This means that each interval has a width of 75/100 = 0.75 minutes.

The probability of a rider waiting in a specific interval can be found by dividing the width of the interval by the total width of the distribution. So, the probability of a rider waiting in a specific interval is 0.75/75 = 0.01.

Therefore, the distribution of the random variable T is a discrete uniform distribution, where each interval has a probability of 0.01.