As a portfolio manager I evaluate the stock-weights in a portfolio and I want only those stocks that can perform better during inflation. By probability distribution, I can distribute their probability of performing during inflation by reviewing the historical data. Hence, we can easily collate the probable returns. Probability distributions is covered under Quants-I for the FRM-I curriculum and the total quantitative analysis has 20% weightage in the FRM-I exam.

Practically probability distributions and scenario analysis is done in a business to predict future levels of sales. It is impossible to predict the exact value of future sales level; businesses however still need to plan for future events. Using probability distribution can help a company frame its possible future values in terms of possible sales level and predict best and worst case scenario. Thus, a company can make its business plans on the likely scenario but still be aware of the alternative possibilities, as well. For better understanding of probability distributions, it’s important to understand variables and random variables. Let’s start with understanding what a variable is.

A variable is a symbol (A, B, x, y, etc.) that can take on any of a specified set of values and Random Variables are a function or a rule which maps each event in a sample space to real numbers. For example: If you are tossing a coin: you can get Heads or Tails. Let's consider values of Headsas0 and Tailsas1 and we have a Random Variable "X" For Random Variable X the possible values would be 0 and 1, in other words X = {0, 1}

Random Variable also has two types. The first one being: Discrete Random Variables which is the set of all possible values of the outcome. For Example: If an analyst is asked about the credit cards owned by an individual, it can be counted anything as {0, 1, 2, 3, 4, 5, 6, 7, 8, and 9}. The second one being Continuous Random Variables: The set of possible values taken by a continuous random variable falls in an interval. For Example: The Salary received by the set of people working in the same profile.

We have talked about both probability distribution and variables; now let’s take an example, to understand the relationship between random variables and probability distributions.

Example: Suppose a coin is flipped two times. This statistical experiment can have four possible results: HH, HT, TH, and TT. Now, we consider the variable X which represents the number of Heads that may come from this experiment. The variable X can have the following values 0, 1 or 2. In this example, X is a random variable; because its value is determined by the outcome of a statistical experiment.

Now, considering the same coin flip experiment described above, the table below associates each outcome with its probability, is an example of a probability distribution.

## Number Of Heads |
## Probability |

0 | 0.25 |

1 | 0.50 |

2 | 0.25 |

Both Discrete Probability Distribution and Continuous Probability Distribution have further sub division; let’s have a quick look at Binomial Distribution and Normal Distribution:

The Binomial Distribution is widely used to test statistical probabilities and significance. It’s a good way of visually detecting unexpected values and a useful tool in determining permutations, combinations, and probabilities, where the outcomes can be broken down into two probabilities. Common uses of binomial distributions in business include quality control, public opinion surveys, medical research, and insurance problems. It can be applied to complex processes such as sampling items in factory production lines or to estimate percentage failure rates of products and components.

In statistics, an average distribution of values states that, when plotted on a graph, resembles the shape of a bell. The curve formed by a Normal Distribution is called a normal curve, bell curve, normal distribution curve or normal probability curve. It is useful because it’s easy to work with mathematically. The amount by which values vary from one another defines the shape of the normal curve. If most of the values are similar, then the normal curve is a tall and thin bell shape. If there is a lot of variation among the values, then the normal curve is a short and wide bell shape. One measure of the variation among values is called the standard deviation.

Global Association of Risk Professionals, Inc. (GARP®) does not endorse, promote, review or warrant the accuracy of the products or services offered by Edu for FRM® related information, nor does it endorse any pass rates claimed by the provider. Further, GARP is not responsible for any fees or costs paid by the user to Edu nor is GARP responsible for any fees or costs of any person or entity providing any services to Edu Study Program. FRM®, GARP® and Global Association of Risk Professionals®, are trademarks owned by the Global Association of Risk Professionals, Inc

CFA Institute does not endorse, promote, or warrant the accuracy or quality of the products or services offered by EduPristine. CFA Institute, CFA®, Claritas®, and Chartered Financial Analyst® are trademarks owned by CFA Institute.

Utmost care has been taken to ensure that there is no copyright violation or infringement in any of our content. Still, in case you feel that there is any copyright violation of any kind please send a mail to legal@edupristine.com and we will rectify it.

Popular Blogs: Whatsapp Revenue Model | CFA vs CPA | CMA vs CPA | ACCA vs CPA | CFA vs FRM

2015 © Edupristine. ALL Rights Reserved.