Understanding Uniform Continuous Random Variables

This video tutorial demonstrates how to calculate the probability of a uniform continuous random variable by hand and verify the result using Desmos. The random variable X is uniformly distributed between 9 and 19. The video explains the probability density function and calculates the probability that X is greater than 14 and less than 16. The manual calculation is verified using the Desmos graphing calculator, showing the consistency of the result.

What is the purpose of this video tutorial?

• To learn about discrete random variables

• To understand the binomial theorem

• To determine probabilities for uniform continuous random variables

• To explore the concept of normal distribution

What are the minimum and maximum values of the random variable x in this tutorial?

• 0 and 10

• 10 and 20

• 5 and 15

• 9 and 19

How is the probability density function (PDF) of a uniform distribution defined?

• As a vertical line

• As a curve

• As a horizontal line

• As a diagonal line

What is the formula for the probability density function in this example?

• f(x) = 1/15

• f(x) = 1/20

• f(x) = 1/10

• f(x) = 1/5

What is the probability that x is greater than 14 and less than 16?

• 0.4

• 0.3

• 0.2

• 0.1

How do you calculate the area under the probability density function for a uniform distribution?

• Using the formula base plus height

• Using the formula base times height

• Using the formula base divided by height

• Using the formula height minus base

What tool is used to verify the probability calculation in this tutorial?

• Excel

• Python

• Desmos

• R

What is the first step in using Desmos to verify the probability?

• Calculate the mean

• Enter the probability value

• Draw the graph manually

• Click on the graphing calculator

What is the result of the probability verification using Desmos?

• 0.2

• 0.4

• 0.1

• 0.3

What does the area of the rectangle in the graph represent?

• The mean of the distribution

• The variance of the distribution

• The standard deviation of the distribution

• The probability that x is greater than 14 and less than 16