Examples are seen in experiments whose sample space is encoded through discrete random variables, in which the distribution can be given by a probability mass function; experiments whose sample space is nonnumerical, in which the distribution will be a categorical distribution and experiments with sample spaces encoded by constant random variables, in which the distribution could be specified by a probability density function.

**A List of Probability
Distributions**

**You can find
literally infinitely numerous probability distributions. A list of a few of the
more crucial distributions follows:**

**Chi-Square
Distribution:** this is for usage of determining how near observed quantities
fit a proposed model

**Binomial
Distribution:** this provides the number of successes for a number of
independent experiments with two outcomes

**Normal Distribution:**
this is known as the bell curve and is found during statistics.

**F-Distribution:**
this is actually a distribution that is employed in analysis of variance
(ANOVA)

**Student's t
Distribution:** this is for utilize with small sample sizes from a normal
distribution

You can find two types of probability distributions:

**1. Discrete
probability distributions**

The probability distribution of any discrete random variable is a listing of probabilities related to each of its possible values. It is also occasionally referred to as probability mass function or the probability function.

More formally, the probability distribution of any discrete random variable X is actually a function which provides the probability f(x) that the random variable equates to x, for each value x:

**f(x) = P(X=x) **

**2. Continuous
probability distributions**

Explain an unbroken continuum of possible occurrences. A random variable is constant if it can consider any value in an interval. The number of possible values in an array is infinite, so the Probability(of a single value) = 0

The mean of a discrete random variable X is actually a weighted average from the possible values that the random variable can consider. Unlike the sample mean of a group of observations, which provides each observation equivalent weight, the mean of a random variable weights each end result xi based on its probability, pi. The common symbol for that mean (also referred to as the expected value of X) is µ.

The mean of any random variable gives the long run average of the variable or the expected average end result over many observations.

**Mean of probability
distribution is given by:**

Sum x*P(x) = 1*0.2 + 2*0.1 + 3*0.35 + 4*0.05 + 5*0.3 = 3.15

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