Understanding Uniform Distribution and Probability

The video tutorial explains the concept of uniform distribution using the example of a metro train's waiting time. It introduces random variable notation and demonstrates how to calculate probabilities for different waiting times. The tutorial also shows how to verify these calculations using Desmos, a graphing calculator tool.

What is the time interval during which the city metro train runs every 15 minutes?

• 9 pm to 6 am

• 6 am to 9 am

• 6 pm to 9 pm

• 9 am to 6 pm

In a uniform distribution, what is the probability density function for a range from 0 to 15?

• 1/10

• 1/15

• 1/25

• 1/20

How would you express the event where the waiting time is less than 12 minutes using random variable notation?

• x ≥ 12

• x < 12

• x = 12

• x > 12

What is the probability that a passenger waits less than 5 minutes for the train?

• 0.80

• 0.33

• 0.67

• 0.53

What is the probability that the waiting time is less than 12 minutes?

• 0.67

• 0.33

• 0.80

• 0.53

If the waiting time is more than 5 minutes, what is the probability?

• 0.80

• 0.53

• 0.67

• 0.33

What is the probability that the waiting time is between 4 and 12.5 minutes?

• 0.47

• 0.77

• 0.67

• 0.57

Which tool is used to verify the calculated probabilities?

• Excel

• Python

• R

• Desmos

What is the graphical representation of a uniform distribution?

• A horizontal line

• A vertical line

• A diagonal line

• A curved line

What is the total area under the probability density function for a uniform distribution?

• 2

• 1.5

• 1

• 0.5