 # Probability Distribution Case Study

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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…show more content…
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…show more content…
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