A bus arrives every 10 minutes at a bus stop. It is assumed...

Name: Problem 22, Chapter 6: Probability and Statistics for Engineers and Scientists
Uploaded: 2025-07-07T15:42:18-08:00
Duration: 45 s
Channel: Hoan Nguyen
Description: A bus arrives every 10 minutes at a bus stop. It is assumed that the waiting time for a particular individual is a random variable with a continuous uniform distribution. (a) What is the probability that the individual waits more than 7 minutes? (b) What is the probability that the individual waits between 2 and 7 minutes?

A bus arrives every 10 minutes at a bus stop. It is assumed that the waiting time for a particular individual is a random variable with a continuous uniform distribution. (a) What is the probability that the individual waits more than 7 minutes? (b) What is the probability that the individual waits between 2 and 7 minutes?

A bus arrives every 10 minutes at a bus stop. It is assumed that the waiting time for a particular individual is a random variable with a continuous uniform distribution.
(a) What is the probability that the individual waits more than 7 minutes?
(b) What is the probability that the individual waits between 2 and 7 minutes?

Key Concepts

Continuous Uniform Distribution

This concept refers to a probability distribution in which all outcomes within a given continuous interval are equally likely. In such a distribution, the probability density function is constant over the interval, and probabilities are determined by the proportion of the interval's length that a particular sub-interval represents.

Random Variables

A random variable is a function that assigns a numerical value to each outcome in a sample space, allowing for the quantification and analysis of uncertainty. In the context of waiting times or any measurable quantity, random variables help in formulating and solving probability problems.

Probability Calculation over Intervals

This concept involves computing the probability that a continuous random variable falls within a specific interval by integrating the probability density function over that interval. For uniform distributions, this calculation simplifies to finding the ratio of the interval length of interest to the total length of the distribution's interval.

Cumulative Distribution Function (CDF)

The CDF of a continuous random variable gives the probability that the variable will take a value less than or equal to a given number. In uniform distributions, the CDF increases linearly over the interval, directly relating sub-interval lengths to cumulative probabilities.

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