Density function for continuous random variables

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Start date Sep 26, 2011
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Continuous Density Density function Function Random Random variables Variables

In summary, a density function for continuous random variables is a function that describes the probability distribution of a continuous random variable. It is different from a probability distribution function, which is used for discrete random variables. The area under a density function can be calculated using integration, and it is also known as the cumulative distribution function. A density function is also referred to as a probability density function and cannot take on negative values, but the integral of a density function can be negative.

Sep 26, 2011

cue928

For the density function for random variable Y:
f(y) = cy^2 for 0<= y <= 2; 0 elsewhere
We are asked to find the value of c. I did a definite integral from 0 to 2 of cy^2. I get c = 3/8. Why would the book show an answer of c = 1/8? Is this an error on their part or am I missing something stupid?

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Sep 26, 2011

nonequilibrium

Indeed, I also think it's an error in the book.

FAQ: Density function for continuous random variables

What is a density function for continuous random variables?

A density function for continuous random variables is a function that describes the probability distribution of a continuous random variable. It shows the relative likelihood of obtaining a particular value or range of values for the variable.

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

A density function is a continuous function that describes the probability distribution of a continuous random variable, while a probability distribution function is a discrete function that describes the probability distribution of a discrete random variable. In other words, a density function is used for continuous variables, while a probability distribution function is used for discrete variables.

How do you calculate the area under a density function?

To calculate the area under a density function, you can use integration. The integral of the density function over a particular interval gives the probability that the random variable falls within that interval. This is also known as the cumulative distribution function (CDF) for continuous random variables.

What is the relationship between a density function and a probability density function?

A density function is another term for a probability density function (PDF). Both terms refer to the same concept of a function that describes the probability distribution of a continuous random variable.

Can a density function take on negative values?

No, a density function cannot take on negative values. The values of a density function must be non-negative, as it represents the relative likelihood of obtaining a certain value for the random variable. However, the integral of a density function can be negative, as it represents the probability of the random variable falling within a certain interval.