Is Y Normally Distributed with Mean \mu and Variance \sigma^2?

Thread starter fireboy420
Start date Oct 19, 2010
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Density Density function Function Probability Probability density Probability density function

In summary, a probability density function (PDF) is a statistical concept used to describe the probability distribution of a continuous random variable. It represents the relative likelihood of different outcomes for a random variable and is used to calculate the probability of a random variable falling within a certain range of values. A PDF differs from a probability mass function (PMF) in that it is used for continuous random variables, while a PMF is used for discrete random variables. The area under a PDF is equal to 1, as the total probability of all possible outcomes is 100%. PDFs are commonly used in statistics to model and analyze continuous data and cannot be negative.

Oct 19, 2010

fireboy420

normally distributed random variable with mean m and variance σ2. Find the PDF of Y

Last edited: Oct 20, 2010

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Oct 20, 2010

statdad

Homework Helper

Is it Y that is normally distributed with mean [tex] \mu [/tex] and variance [tex] \sigma^2 [/tex]? If so, why is there any question about Y's pdf? Are you leaving out some of the information?

What is a probability density function (PDF)?

A probability density function (PDF) is a statistical concept used to describe the probability distribution of a continuous random variable. It is a function that represents the relative likelihood of different outcomes for a random variable.

How is a probability density function different from a probability mass function?

A probability density function (PDF) is used to describe the distribution of continuous random variables, while a probability mass function (PMF) is used for discrete random variables. This means that a PDF gives the probability of a random variable falling within a certain range of values, while a PMF gives the probability of a random variable taking on a specific value.

What is the area under a probability density function?

The area under a probability density function (PDF) is equal to 1, as the total probability of all possible outcomes for a continuous random variable is 100%. This means that the PDF can be used to calculate the probability of a random variable falling within a certain range of values.

How is a probability density function used in statistics?

Probability density functions (PDFs) are used in statistics to model and analyze continuous data. They are useful for determining the likelihood of a particular outcome, calculating probabilities for a range of values, and making predictions based on data.

Can a probability density function be negative?

No, a probability density function (PDF) cannot be negative. The values of a PDF must be non-negative, as it represents the relative likelihood of different outcomes for a random variable. A negative probability would not make sense in this context.