Probability Distribution Case Study

Why we use Probability Distribution:
Some uses of probability distribution are as follows:
Scenario Analysis
Probability distributions can be used to create scenario analyses. A scenario analysis uses probability distributions to create several, theoretically distinct possibilities for the outcome of a particular course of action or future event. For example, a business might create three scenarios: worst-case, likely and best-case. The worst-case scenario would contain some value from the lower end of the probability distribution; the likely scenario would contain a value towards the middle of the distribution; and the best-case scenario would contain a value in the upper end of the scenario.
Sales Forecasting
One practical use for probability

The two basic types of random variables are discrete random variables and continuous random variables. A discrete random variable can take on at most a countable number of possible values. For example, a discrete random variable X can take on a limited number of outcomes X1,X2,X3,…..,Xn (n possible outcomes), or a discrete random variable Y can take on an unlimited number of outcomes Y1, Y2, Y3, …. (without end) because we can count all the possible outcomes of X and Y (even if we go on forever in the case of Y), both X and Y satisfy the definition of a discrete random variable. By contrast, we cannot count the outcomes of a continuous random

We can view a probability distribution in two ways. The basic view is the Probability function, which specifies the probability that the random variable takes on a specific value: P(X=x) is the probability that a random variable X takes on a specific value x. (Note that capital X represents the random variable and lowercase x represents a specific value that the random variable may take). For a discrete random variable, the shorthand notation for the probability function is p(x) = P (X=x). For continuous random variables, the probability function is denoted f(x) and called the probability density function.
Properties of discrete random variable:
A probability function has two key properties: 0 ≤ p(x) ≤ 1, because probability is a number between 0 and 1 The sum of the properties p(x) over all values of X equals 1. If we add up the probabilities of all the distinct possible outcomes of a random variable, that the sum equals 1.
Example:
A coin toss has only two possible outcomes: heads or tails and taking a test could have two possible outcomes: Head or tail.
The discrete possibilities of head can be as