This document provides an introduction to probability concepts. It defines probability as the chance of an event occurring and lists some key rules, such as the probabilities of all possible outcomes must sum to 1. It describes the normal probability distribution as a bell-shaped curve that is symmetric around the expected rate of return. It then discusses skewness and kurtosis as measures of the asymmetry and peakedness of a distribution.

1. Module - 59
Introduction to
Accounting
CMT LEVEL - I

2. Probability
• The total probabilities of an event occurring or not will always
equal 100 percent. If you have a 10 percent probability that
something may happen, then you have a 90 percent
probability that it won’t.
• The simplest example is the coin toss. You have a 50 percent
probability that the coin will land on either side because only
two options exist.
• When you apply probability theory to the standard deviation,
you end up with something called a normal distribution.

3. Probability
• Probability: chance of an event taking place
Rules relating to probabilities
• If an out come is definitely certain to happen, its probability is
1
• The probability of an event happening would mostly lie
between 0 and 1
• Sum of probabilities of an event happening must be equal to 1
• Probability can never be a negative number
• Possible outcomes must be mutually exclusive

4. Probability Distribution
• A probability Distribution is a table showing the various
possible outcomes of an event along with their respective
probabilities
• Normal Probability Distribution is a bell shaped curve, and is
perfectly symmetric around the expected rate of return
which is in the middle
Band Probability
± One standard derivation (ó) 68.3%
± Two standard Derivation (ó) 95.4%
± Three standard deviation (ó) 99.7%

5. Skewness
• The third central moment is a measure of the lopsidedness
of the distribution; any symmetric distribution will have a
third central moment, if defined, of zero.
•The normalised third central moment is called the skewness,
often γ.
• A distribution that is skewed to the left (the tail of the
distribution is longer on the left) will have a negative
skewness.

6. Skewness
• A distribution that is skewed to the right (the tail of the
distribution is longer on the right), will have a positive
skewness.
• For a calculated skew number (average cubed deviations
divided by the cubed standard deviation),
• For evaluate whether a return is positively skewed (skew >
0), negatively skewed (skew < 0) or symmetric (skew = 0).

7. Kurtosis
•Kurtosis refers to the degree of peak in a distribution.
More peak than normal (leptokurtic) means that a
distribution also has fatter tails and that there are
lesser chances of extreme outcomes compared to a
normal distribution.
•It is sometimes referred to as the "volatility
of volatility.“

8. Kurtosis
• A statistical measure used to describe the distribution of
observed data around the mean.
• Used generally in the statistical field, kurtosis describes
trends in charts.
• A high kurtosis portrays a chart with fat tails and a low, even
distribution, whereas a low kurtosis portrays a chart with
skinny tails and a distribution concentrated toward the
mean.