- #1
blahblah8724
- 32
- 0
What is the difference between a probability mass function and a probability measure or are they just the same thing?
Thanks!
Thanks!
blahblah8724 said:What is the difference between a probability mass function and a probability measure or are they just the same thing?
Thanks!
A PMF is a function that maps each possible outcome of a random variable to its probability of occurrence. It is used for discrete random variables, meaning that the possible outcomes are countable. On the other hand, a Probability Measure is a function that assigns a probability to a set of possible outcomes in a sample space. It is used for continuous random variables, meaning that the possible outcomes are uncountable.
To calculate the probability using a PMF, you need to know the value of the random variable and the corresponding probability of that value occurring. You can then multiply the value of the random variable by its probability to get the probability of that specific outcome occurring.
No, a PMF cannot take on negative values. The probabilities assigned by a PMF must be non-negative and sum to 1. This is because probabilities represent the likelihood of an event occurring, and a negative probability would not make sense in this context.
A Probability Measure assigns probabilities to sets of outcomes, while a CDF gives the probability that a random variable is less than or equal to a specific value. In other words, a CDF is a function that maps values of a random variable to their cumulative probabilities, while a Probability Measure maps sets of outcomes to their probabilities.
No, a PMF can only be used for discrete random variables. For continuous random variables, a Probability Density Function (PDF) is used instead, which gives the probability of a random variable taking on a specific value. The area under the PDF curve between two values represents the probability of the random variable falling within that range.