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Probability
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Head-Head Head-Tail Tail-Head Tail-Tail Other possibility
Let's examine the result of rolling two conventional six-sided dice as a straightforward illustration of a probability
distribution. A roll of any single number from one to six has a 1/6 probability on each die, however, the aggregate
of two dice will provide the probability distribution shown in the image below. The most frequent result is seven
(1+6, 6+1, 5+2, 2+5, 3+4, 4+3). Two and twelve, on the other hand, are much less likely (1+1 and 6+6).
2.2. TYPES OF DISTRIBUTIONS
In data science, types of distributions are solely based on what type of data we can encounter with while solving
problems.
The data can be classified into two types:
• Discrete Data: It refers to the data that accepts only particular values. For example, if you take a test, you can
pass or fail in it. Since there are only two possible outcomes, the data in this case is discrete.
• Continuous Data: It refers to the data that can accept any value within a range. This range of values will have a
lower bound and an upper bound, which we call the minimum and the maximum possible values. For example,
the width of a road, the weight of a person, or the depth of an ocean.
So based on type of data, distribution can be of two types:
• Discrete probability distributions
• Continuous probability distributions
Let us discuss these in detail.
2.2.1. Discrete Probability Distributions
As its name suggests, a discrete probability distribution is a distribution where observation can take only a finite
number of values. It is expressed with a formula (Density Function) describing the shape of the distribution. These
are usually described with a frequency distribution table, or other type of graph or chart. For example, the following
chart shows the probability of rolling a die. All of the die rolls have an equal chance of being rolled (one out of six,
or 1/6). This gives you a discrete probability distribution of:
Distributions in Data Science 139

