Question regarding a probability mass function of a random variable

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Thread starter dylbester
Start date Mar 14, 2016
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Function Mass Probability Random Random variable Variable

In summary, a probability mass function (PMF) is a mathematical function that assigns a probability to each possible outcome of a discrete random variable. It is different from a probability density function (PDF) in that it is used for discrete random variables and gives the exact probability of a specific outcome. A PMF must satisfy two properties - the assigned probabilities must be between 0 and 1, and the sum of all probabilities must equal 1. It can be used to calculate the probability of a specific outcome or range of outcomes by summing the probabilities within the desired range. A PMF cannot be used for continuous random variables, for which a PDF is used instead.

Mar 14, 2016

dylbester

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Thank you for your time, I really appreciate it

I have no idea where to even begin

Last edited: Mar 14, 2016

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Mar 14, 2016

Evgeny.Makarov

Gold Member

MHB

dylbester said:

I have no idea where to even begin

You should begin with the definition of mean and variance, and also with finding $p(0)$ and $p(1)$.

1. What is a probability mass function (PMF)?

A probability mass function is a mathematical function that describes the probability distribution of a discrete random variable. It assigns a probability to each possible outcome of the random variable.

2. How is a PMF different from a probability density function (PDF)?

A PMF is used for discrete random variables, whereas a PDF is used for continuous random variables. A PMF gives the exact probability of a specific outcome, while a PDF gives the probability density at a given point.

3. What are the properties of a PMF?

A PMF must satisfy two properties: 1) The probability assigned to each outcome must be between 0 and 1, and 2) The sum of all probabilities must equal 1.

4. How can a PMF be used to calculate probabilities?

A PMF can be used to calculate the probability of a specific outcome or a range of outcomes. This is done by summing the probabilities of all the outcomes within the desired range.

5. Can a PMF be used for continuous random variables?

No, a PMF is only used for discrete random variables. For continuous random variables, a probability density function (PDF) is used to describe the probability distribution.