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Probability Theory Update

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Random Variable

Random event:

A random event is an event whose outcome can not be predicted. Rolling a die or tossing a coin can be examples.

Random variable:

A random variable is a variable whose value is we don't know.

A random variable is used to quantify the output of the random event. We can define a random variable as s capital letter; let it be X in our example.

Example:

We were rolling a die two times and received numbers 3 and 5; so, we can say that a random variable is X = 3 + 5 =8.

Simulating a random variable with Python:

To simulate an experiment in Python we will use the function from the NumPy library: .choice(values, size = size, replace = True)

  • values - a list of possible outcomes of the event.

  • size - the number of times we repeat the experiment.

  • replace = True - it can be equal to False, but in this course, we will not change this parameter.

The experiment of rolling a six-sided die five times.

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import numpy as np experiment = np.random.choice(range(1,7), size = 5, replace = True) random_value = sum(experiment) print("The outcomes of the experiment are:", experiment) print("The Random value is equal to:", random_value)
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SectionΒ 3. ChapterΒ 1

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book
Random Variable

Random event:

A random event is an event whose outcome can not be predicted. Rolling a die or tossing a coin can be examples.

Random variable:

A random variable is a variable whose value is we don't know.

A random variable is used to quantify the output of the random event. We can define a random variable as s capital letter; let it be X in our example.

Example:

We were rolling a die two times and received numbers 3 and 5; so, we can say that a random variable is X = 3 + 5 =8.

Simulating a random variable with Python:

To simulate an experiment in Python we will use the function from the NumPy library: .choice(values, size = size, replace = True)

  • values - a list of possible outcomes of the event.

  • size - the number of times we repeat the experiment.

  • replace = True - it can be equal to False, but in this course, we will not change this parameter.

The experiment of rolling a six-sided die five times.

1234567891011
import numpy as np experiment = np.random.choice(range(1,7), size = 5, replace = True) random_value = sum(experiment) print("The outcomes of the experiment are:", experiment) print("The Random value is equal to:", random_value)
copy

Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
Everything was clear?

How can we improve it?

Thanks for your feedback!

SectionΒ 3. ChapterΒ 1
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