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Questions and Answers
What is the main difference between a probability density function and a probability mass function?
What is the main difference between a probability density function and a probability mass function?
- The range of the variable
- The method of calculation
- The number of possible outcomes
- The type of random variable it represents (correct)
Which of the following is a characteristic of a probability density function?
Which of the following is a characteristic of a probability density function?
- The area under the curve is equal to 1 (correct)
- The function can be negative
- The function must be continuous
- The function must be differentiable
What is the purpose of normalizing a probability density function?
What is the purpose of normalizing a probability density function?
- To ensure the area under the curve is equal to 1 (correct)
- To ensure the function is continuous
- To ensure the function can be negative
- To ensure the function is differentiable
Which of the following is an example of a continuous random variable?
Which of the following is an example of a continuous random variable?
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What is the relationship between the probability density function and the cumulative distribution function?
What is the relationship between the probability density function and the cumulative distribution function?
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Study Notes
Probability Density Function vs. Probability Mass Function
- A probability density function (PDF) is used for continuous random variables, whereas a probability mass function (PMF) is used for discrete random variables.
Characteristics of a Probability Density Function
- A probability density function (PDF) is a non-negative function that satisfies the property that the integral over the entire range of the variable is equal to 1.
- The area under the curve of a PDF represents the probability of the event.
Normalizing a Probability Density Function
- The purpose of normalizing a probability density function is to ensure that the total probability over all possible values of the random variable is equal to 1.
Examples of Continuous Random Variables
- The time until a component fails is an example of a continuous random variable.
- The height of a person in a population is another example of a continuous random variable.
Probability Density Function and Cumulative Distribution Function
- The cumulative distribution function (CDF) is the integral of the probability density function (PDF) from negative infinity to a specific point.
- The PDF can be obtained by differentiating the CDF with respect to the variable.
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