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Do some normal probability distributions have different arithmetic means and different standard deviations?
Yes. Most do.
What is the difference between a binomial probability and piossion Probability?
Assuming that "piossion" refers to Poisson, they are simply different probability distributions that are applicable in different situations.
What is probability mass function?
It is a function which is usually used with continuous distributions, to give the probability associated with different values of the variable.
Do some normal probability distributions have different means and different standard deviations?
Yes. Normal (or Gaussian) distribution are parametric distributions and they are defined by two parameters: the mean and the variance (square of standard deviation). Each pair of these parameters gives rise to a different normal distribution. However, they can all be "re-parametrised" to the standard normal distribution using z-transformations. The standard normal distribution has mean 0 and variance 1.
What is the difference between arithmetic mean and mode?
The mean, median, and mode are all measures of central tendency. For symmetrical distributions they all have the same value. For assymetrical distributions they have different values. The mean is the average and the mode is the most likely value.
