5 Questions
Which of the following best describes a discrete random variable?
A random variable that can take on only a finite number of values.
What can be determined from a probability mass function?
The probability of occurrence of each value of a discrete random variable.
What is the purpose of a cumulative distribution function?
To determine the probability of occurrence of each value of a discrete random variable.
What can be calculated using a cumulative distribution function?
The probability of a random variable being less than or equal to a given value.
What assumptions are necessary for each discrete probability distribution?
The assumption that the random variable can take on only a finite number of values.
Study Notes
Discrete Random Variables
- A discrete random variable is a variable that can only take on specific, distinct values
Probability Mass Function (PMF)
- A PMF describes the probability of each distinct value of a discrete random variable
- From a PMF, you can determine:
- The probability of each possible value of the discrete random variable
- The probability of a range of values of the discrete random variable
Cumulative Distribution Function (CDF)
- The purpose of a CDF is to describe the cumulative probability of a discrete random variable
- A CDF describes the probability that a discrete random variable takes on a value less than or equal to a given value
- Using a CDF, you can calculate:
- The probability that a discrete random variable takes on a value within a certain range
- The probability that a discrete random variable takes on a value less than or equal to a certain value
Discrete Probability Distributions
- Each discrete probability distribution has its own set of assumptions that must be met in order to use the distribution
- Examples of discrete probability distributions include the Binomial, Poisson, and Hypergeometric distributions
- Assumptions necessary for each distribution vary, but may include:
- Independence of trials
- Fixed number of trials
- Constant probability of success
- And others, depending on the specific distribution
Test your knowledge on discrete probability distribution with this quiz! Learn how to determine probabilities from probability mass functions and cumulative functions, calculate means and variances for discrete random variables, and understand key assumptions. Prepared by Engr. Jerson A. Culla and Engr. Ladylyn M. Culla.
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