Probability Distribution

Once the data collected it needs to be sorted and analyzed. When the size of the data increases, analyzing them manually becomes impossible. It is then, the statistical tools comes to help. Statistical tools not only help in computing huge data but also its graphical representation helps in better representation of data.

**Basic Statistics:**

The catalyst for better analysis is sound statistics. So Statistics is logical and systematical way of studying the data, organizing them, making analysis of the data, interpret or decode them and finally presenting the data for final use. For such an elaborate process various methods are used for various purposes.

Following are the ways of studying, computing and presenting statistics:

• Probability

• Random variables

• Probability distribution

• The Central Limit Theorem

• Sampling and statistical inference

• Confidence intervals

• Hypothesis testing

The catalyst for better analysis is sound statistics. So Statistics is logical and systematical way of studying the data, organizing them, making analysis of the data, interpret or decode them and finally presenting the data for final use. For such an elaborate process various methods are used for various purposes.

Following are the ways of studying, computing and presenting statistics:

• Probability

• Random variables

• Probability distribution

• The Central Limit Theorem

• Sampling and statistical inference

• Confidence intervals

• Hypothesis testing

PROBABILITY

It is the numerical way of depicting how probable an event is likely to offer. The process is often determined using set theory. The purpose is to analyze past data to find a pattern, assuming that past is a reflection of future.

• Set operations

Union (A U B)

Intersection (A B)

• Venn diagrams

Basic operations on Venn diagrams

• Basic probability axioms

P (S) = 1

P (A) >= 0 for all A S

P (A U B) = P(A) + P(B) –P (A B)

• Conditional probability

P(A|B) = P (A B)/ P(B)

• Bayes theorem

• Set operations

Union (A U B)

Intersection (A B)

• Venn diagrams

Basic operations on Venn diagrams

• Basic probability axioms

P (S) = 1

P (A) >= 0 for all A S

P (A U B) = P(A) + P(B) –P (A B)

• Conditional probability

P(A|B) = P (A B)/ P(B)

• Bayes theorem

Random Variables

It’s a function or a rule which maps each event in a sample space to real numbers. For example:

Question: Suppose there are 8 balls in a bag. The random variable X is the weight, in lb, of a ball selected at random. Balls 1, 2 and 3 weigh 0.1lb, balls 4 and 5 weigh 0.15lb and balls 6, 7 and 8 weigh 0.2lb. Using the notation above, write down this information.

Solution: X(b1) = 0.10 lb, X(b2) = 0.10 lb, X(b3) = 0.1 lb,

X(b4) = 0.15 lb, X(b5) = 0.15 lb

X(b6) = 0.2 lb, X(b7) = 0.2 lb

There are two types of Random Variables

• Discrete Random Variables: The set of all possible values of the outcome. For Example:

Credit cards owned by an individual = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

• Continuous Random Variables: The set of possible values taken by a continuous random variable falls in an interval. For Example: Salary of a set of individuals

Question: Suppose there are 8 balls in a bag. The random variable X is the weight, in lb, of a ball selected at random. Balls 1, 2 and 3 weigh 0.1lb, balls 4 and 5 weigh 0.15lb and balls 6, 7 and 8 weigh 0.2lb. Using the notation above, write down this information.

Solution: X(b1) = 0.10 lb, X(b2) = 0.10 lb, X(b3) = 0.1 lb,

X(b4) = 0.15 lb, X(b5) = 0.15 lb

X(b6) = 0.2 lb, X(b7) = 0.2 lb

There are two types of Random Variables

• Discrete Random Variables: The set of all possible values of the outcome. For Example:

Credit cards owned by an individual = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

• Continuous Random Variables: The set of possible values taken by a continuous random variable falls in an interval. For Example: Salary of a set of individuals

Discrete Probability Distributions

Uniform: The discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed.
Example: Assigning equal probability of default to a portfolio of credit card holders

Bernoulli: A Bernoulli trial is an experiment which has only two possible outcomes S (success) and f (failure). Examples: Tossing of a coin. "Head" corresponds to "success" and "Tail" corresponds to "failure"

Binomial: The probability of getting exactly " K " successes in " N " trials is given by the probability mass function.

Bernoulli: A Bernoulli trial is an experiment which has only two possible outcomes S (success) and f (failure). Examples: Tossing of a coin. "Head" corresponds to "success" and "Tail" corresponds to "failure"

Binomial: The probability of getting exactly " K " successes in " N " trials is given by the probability mass function.

Continuous Probability Distributions

Edupristine has an array of theories, examples, case study, videos to help you learn each of these concepts in details. Write an email to us at help@edupristine.com for an easy access to a wide spectrum of knowledge.

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.