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There are probably many probability distributions that have just one parameter. The most important one for statistical analysis is probably the Student t distribution.This probability distribution is fully described by a single parameter which is often called "degrees of freedom". The parameter describes the scale of the distribution, and not the location, since the Student t distribution is always centered at zero (unlike the normal distribution, which has a scale parameter, the variance, and a location parameter, the mean).Another example of a distribution that is described with a single parameter is the exponential distribution. Unlike the Student t distribution, it is a distribution that takes only positive values.
Yes. When we refer to the normal distribution, we are referring to a probability distribution. When we specify the equation of a continuous distribution, such as the normal distribution, we refer to the equation as a probability density function.
The statement is true that a sampling distribution is a probability distribution for a statistic.
No, it is the name given to the Gaussian distribution.
The exponential distribution and the Poisson distribution.