Poisson distribution
Poisson distribution is discrete (like the binomial) because the values that can take the random variable are natural numbers, although in the Poisson distribution all the possible cases are theoretically infinite.
Poisson distribution is characterized by a single parameter lambda. Its mean is lambda and its variance is also lambda.
The mean is represented by a triangle and it can be seen as a point of equilibrium. Dragging it we modify the lambda parameter.
We can show a normal curve that has the same mean and variance that the Poisson distribution. This normal curve approximate the Poisson distribution in some cases.
The gray dots control vertical and horizontal scales. Pressing and dragging the right button we can move the graphic left and right.
LINKS
|
Binomial distribution
When modeling a situation where there are n independent trials with a constant probability p of success in each test we use a binomial distribution.
|
|
Normal approximation to Binomial distribution
In some cases, a Binomial distribution can be approximated by a Normal distribution with the same mean and variance.
|
|
Normal distribution
The Normal distribution was studied by Gauss. This is a continuous random variable (the variable can take any real value). The density function is shaped like a bell.
|
|
One, two and three standar deviations
One important property of normal distributions is that if we consider intervals centered on the mean and a certain extent proportional to the standard deviation, the probability of these intervals is constant regardless of the mean and standard deviation of the normal distribution considered.
|
|
Calculating probabilities in Normal distributions
It may be interesting to familiarize ourselves with the probabilities correspondig to different intervals in normal distributions.
|
|
Student's t-distributions
Student's t-distributions were studied by William Gosset(1876-1937) when working with small samples.
|
|