Understanding Uniform Distribution

The video tutorial explains how to determine the probability of a random variable x being greater than 7 and less than 10 in a uniform distribution between 6 and 11. It uses a graph to illustrate the probability density function and calculates the probability using two methods: dividing the area into rectangles and using the base times height formula. The tutorial emphasizes understanding the uniform distribution and applying mathematical formulas to solve probability problems.

What is the range of the uniform distribution discussed in the video?

• 5 to 12

• 7 to 10

• 6 to 11

• 0 to 5

What does the horizontal line in the graph represent?

• Exponential distribution

• Normal distribution

• Binomial distribution

• Uniform distribution

What is the total area of the distribution rectangle?

• 2

• 1.5

• 1

• 0.5

How many equally sized pieces are shaded blue in the rectangle?

• 4

• 3

• 5

• 2

What is the probability that x is greater than 7 and less than 10?

• 0.3

• 0.6

• 0.4

• 0.5

What is the formula for the probability density function f(x) in this context?

• a/b

• b-a

• 1/(b-a)

• b/a

What is the height of the rectangle in the base times height method?

• 1/3

• 1/4

• 1/5

• 1/6

What is the length of the base in the base times height method?

• 2

• 3

• 4

• 5

What is the final probability calculated using both methods?

• 0.7

• 0.4

• 0.5

• 0.6

What is the significance of the area of the blue rectangle?

• It represents the probability of x being greater than 10

• It represents the probability of x being between 6 and 11

• It represents the probability of x being between 7 and 10

• It represents the total distribution