Uniform Distribution

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What is a uniform distribution?

Back

A uniform distribution is a type of probability distribution in which all outcomes are equally likely. In a continuous uniform distribution, the probability density function is constant across the range of possible values.

Tags

CCSS.7.SP.C.7A

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How do you calculate the probability of waiting more than a certain time in a uniform distribution?

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To calculate the probability of waiting more than a certain time in a uniform distribution, use the formula: P(X > a) = (b - a) / (b - c), where 'a' is the time threshold, 'b' is the maximum time, and 'c' is the minimum time.

Tags

CCSS.7.SP.C.7A

Front

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

Back

The probability density function (PDF) of a uniform distribution is given by: f(x) = 1 / (b - a) for a ≤ x ≤ b, where 'a' is the minimum value and 'b' is the maximum value.

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

Front

What is the area under the curve of a uniform distribution?

Back

The area under the curve of a uniform distribution is equal to 1, representing the total probability of all possible outcomes.

Tags

CCSS.7.SP.C.7A

Front

If a shuttle train arrives every 5 minutes, what is the height of the uniform distribution graph?

Back

The height of the uniform distribution graph is 1/5, calculated as 1 divided by the interval length (5 minutes).

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What is the probability that a random variable x has a value greater than a specific number in a uniform distribution?

Back

The probability that a random variable x has a value greater than a specific number can be calculated as the area of the rectangle formed by the remaining interval.

Tags

CCSS.7.SP.C.7A

Front

What type of random variable is the number of points scored by a basketball team?

Back

The number of points scored by a basketball team is a discrete random variable, as it can only take on specific integer values.

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How do you represent a uniform distribution graphically?

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A uniform distribution is represented graphically as a rectangle where the height is constant and the width represents the range of values.

Front

What is the probability of waiting more than 18 minutes for a train that leaves every 30 minutes?

Back

The probability of waiting more than 18 minutes is 2/5, calculated as (30 - 18) / 30.

Tags

CCSS.HSS.MD.B.6

CCSS.HSS.MD.B.7

Front

What is the relationship between the area of a rectangle and probability in a uniform distribution?

Back

In a uniform distribution, the area of the rectangle represents the probability of the random variable falling within a specific range.

Tags

CCSS.7.SP.C.7A