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Added terms and probability-distributions folders and file #5914

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Added terms and probability-distributions folders and file
SaraVKeene Jan 3, 2025
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Merge branch 'main' into probability-distributions
PragatiVerma18 Jan 10, 2025
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PragatiVerma18 Jan 11, 2025
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44 changes: 44 additions & 0 deletions content/scipy/concepts/scipy-stats/terms/probability-distributions.md
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---
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The file name should be singular - probability-distribution.md. Please fix that.

Title: 'probability-distributions.md'
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The title should be the same as the file name but not with the extension. It should also be in the title case.

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Title: 'probability-distributions.md'
Title: 'Probability Distribution'

Description: 'This entry provides an introduction to probability distributions, their syntax, and an example using SciPy.'
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The description should be the definition of the concept being explained.

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Description: 'This entry provides an introduction to probability distributions, their syntax, and an example using SciPy.'
Description: 'Probability Distribution is a function that describes the likelihood of different outcomes for a random variable.'

Subjects:
- 'Bash/Shell'
- 'Data Visualization'
- 'Information Technology'
Tags:
- 'Data Structures'
- 'Functions'
- 'Probability'
CatalogContent:
- 'docs/content/scipy/concepts/scipy-stats/terms/probability-distributions/probability-distributions.md'
- 'Python:SciPy'
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These are not valid catalog content resources, please refer to catalog-content.md for reference.

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- 'docs/content/scipy/concepts/scipy-stats/terms/probability-distributions/probability-distributions.md'
- 'Python:SciPy'
- 'learn-data-science'
- 'paths/data-science-foundations'

---

The element of surprise. **Probability distributions** describe how the structure of random variables are allocated. In the context of SciPy, the scipy.stats module provides various functions for working with different probability distributions that deliver consistent information such as Cumulative Distribution Functions (CDF), Probability Density Functions (PDF), and other statistical metrics.They convey the probabilities of various outcomes, and are fundamental to statistics and data analysis;.
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Please format the text according to the style-guide.md.

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The element of surprise. **Probability distributions** describe how the structure of random variables are allocated. In the context of SciPy, the scipy.stats module provides various functions for working with different probability distributions that deliver consistent information such as Cumulative Distribution Functions (CDF), Probability Density Functions (PDF), and other statistical metrics.They convey the probabilities of various outcomes, and are fundamental to statistics and data analysis;.
**Probability distribution** describes how the values of random variables are distributed. In the context of [SciPy](https://www.codecademy.com/resources/docs/scipy), the `scipy.stats` module provides various functions for working with different probability distributions, offering consistent information such as **Cumulative Distribution Functions (CDF)**, **Probability Density Functions (PDF)**, and other statistical metrics. These distributions convey the probabilities of various outcomes and are fundamental to statistics and data analysis.


## Syntax
from scipy.stats import distribution_name
rv = distribution_name(parameters)
cdf_value = rv.cdf(x)
pdf_value = rv.pdf(x)
pmf_value = rv.pmf(x)
mean_value = rv.mean()
variance_value = rv.var()
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This should be wrapped in code syntax. Add suitable code comments for better understanding.

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from scipy.stats import distribution_name
rv = distribution_name(parameters)
cdf_value = rv.cdf(x)
pdf_value = rv.pdf(x)
pmf_value = rv.pmf(x)
mean_value = rv.mean()
variance_value = rv.var()
```pseudo
from scipy.stats import distribution_name
# Create a random variable object for the distribution
rv = distribution_name(parameters)
# Compute the CDF (Cumulative Distribution Function) at x
cdf_value = rv.cdf(x)
# Compute the PDF (Probability Density Function) at x (for continuous distributions)
pdf_value = rv.pdf(x)
# Compute the PMF (Probability Mass Function) at x (for discrete distributions)
pmf_value = rv.pmf(x)
# Compute the mean of the distribution
mean_value = rv.mean()
# Compute the variance of the distribution
variance_value = rv.var()


## Example: Normal distribution using SciPy
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It should just be Example as heading.

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## Example: Normal distribution using SciPy
## Example

from scipy.stats import norm

rv = norm(loc=0, scale=1)

cdf_value = rv.cdf(1)

pdf_value = rv.pdf(1)

mean_value = rv.mean()

variance_value = rv.var()

print("CDF at x=1:", cdf_value)
print("PDF at x=1:", pdf_value)
print("Mean of the distribution:", mean_value)
print("Variance of the distribution:", variance_value)
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Similar to above comment, add code comments and wrap in code syntax. Also include output and brief explanation for the code.

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from scipy.stats import norm
rv = norm(loc=0, scale=1)
cdf_value = rv.cdf(1)
pdf_value = rv.pdf(1)
mean_value = rv.mean()
variance_value = rv.var()
print("CDF at x=1:", cdf_value)
print("PDF at x=1:", pdf_value)
print("Mean of the distribution:", mean_value)
print("Variance of the distribution:", variance_value)
```py
from scipy.stats import norm
# Create a normal distribution with mean 0 and standard deviation 1
rv = norm(loc=0, scale=1)
# Compute the CDF (Cumulative Distribution Function) at x = 1
cdf_value = rv.cdf(1) # The probability that a value from the distribution is <= 1
# Compute the PDF (Probability Density Function) at x = 1
pdf_value = rv.pdf(1) # The likelihood (height of the curve) at x = 1
# Compute the mean of the distribution
mean_value = rv.mean() # The expected value (center) of the distribution
# Compute the variance of the distribution
variance_value = rv.var() # The measure of spread of the distribution
# Output the results
print("CDF at x=1:", cdf_value)
print("PDF at x=1:", pdf_value)
print("Mean of the distribution:", mean_value)
print("Variance of the distribution:", variance_value)

The output of the above code will be as follows:

CDF at x=1: 0.8413447460685429
PDF at x=1: 0.24197072451914337
Mean of the distribution: 0.0
Variance of the distribution: 1.0