Page 145 - Data Science class 10
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Continuous data can take any value within a given range. The range may be finite or infinite. For example, the
weight or height of a person, the length of the road. The weight of a person can be any value like 60 kg, or 62.5
kg, or 68.9 kg.
Infinite possibilities are possible and there is a chance of seeing a variety of them, which is how continuous
distributions are defined. Every range of values and the likelihood that an observed value will fall within it are listed
in a probability density function.
Continuous distributions are defined by the Probability Density Functions (PDF) instead of Probability Mass
Functions (PMF). The Probability Density Function (PDF) P(x) of a continuous random variable X is defined as the
derivative of the CDF P(x): P(x)=ddxFP(x). The probability that a continuous random variable is equal to an exact
value is always equal to zero. Continuous probabilities are defined over an interval. For example, P(X = 3) = 0 but
P(2.99 < X < 3.01) can be calculated by integrating the PDF over the interval [2.99, 3.01]
Cumulative Distribution Function (CDF) refers to a probability distribution that deals with both continuous and
discrete data.
There are different types of continuous probability distributions:
• Uniform distribution
• Normal distribution
Let us discuss these in detail.
Uniform Distribution
Uniform distribution has both continuous and discrete forms. Let us discuss about them.
Discrete Uniform Distribution
According to statistics and probability theory, a statistical distribution where the probability of outcomes is equally
likely and with finite values is called the discrete uniform distribution. The different outcomes of rolling a 6-sided
die serve as a good illustration of a discrete uniform distribution. There are six possible values: 1, 2, 3, 4, 5, or 6.
Each of the six numbers has an equal chance of occurring in this situation. Therefore, each side of the 6-sided die
has a 1/6 probability each time it is thrown. The number of values is finite. It is impossible to get a value of 1.3, 4.2,
or 5.7 when rolling a fair die.
When plotted on a graph, the distribution is represented as a horizontal line, with each possible outcome captured
on the x-axis, at the fixed point of probability along the y-axis.
Uniform Distribution
One Six-sided Die
20%
15%
10%
5%
0%
1 2 3 4 5 6
Distributions in Data Science 143

