Normal distribution in SciPy - Step-by-Step Execution

Concept Flow - Normal distribution

Start: Define mean (mu) and std dev (sigma)

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Use scipy.stats.norm to create distribution

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Calculate PDF or CDF for values

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Output probabilities or plot

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End

We start by setting the mean and standard deviation, then use scipy to get probabilities or plots for values in the normal distribution.

Execution Sample

SciPy

from scipy.stats import norm
mu, sigma = 0, 1
x = 0
pdf_val = norm.pdf(x, mu, sigma)
print(pdf_val)

This code calculates the probability density at x=0 for a normal distribution with mean 0 and std dev 1.

Execution Table

Step	Variable	Value	Action	Result
1	mu	0	Set mean	mu = 0
2	sigma	1	Set std dev	sigma = 1
3	x	0	Set point to evaluate	x = 0
4	pdf_val	0.3989422804014327	Calculate PDF at x	pdf_val = norm.pdf(0, 0, 1)
5	-	-	Print pdf_val	Output: 0.3989422804014327

💡 All steps done, PDF value computed and printed.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	Final
mu	undefined	0	0	0	0	0
sigma	undefined	undefined	1	1	1	1
x	undefined	undefined	undefined	0	0	0
pdf_val	undefined	undefined	undefined	undefined	0.3989422804014327	0.3989422804014327

Key Moments - 2 Insights

Why do we need to specify mean and standard deviation before calculating PDF?

Because the normal distribution shape depends on mean and std dev. The execution_table rows 1 and 2 show setting these before calculating PDF at step 4.

What does the PDF value represent at x=0?

It shows the height of the normal curve at x=0, not a probability but a density. See execution_table step 4 where pdf_val is calculated.

Visual Quiz - 3 Questions

Look at the execution_table, what is the value of pdf_val at step 4?

A 0.3989

B 1.0

C 0.0

D 0.5

💡 Hint

Check the 'Value' column at step 4 in execution_table.

At which step is the standard deviation set?

A Step 3

B Step 1

C Step 2

D Step 4

💡 Hint

Look at the 'Variable' column for 'sigma' in execution_table.

If we change mu to 1, how does it affect pdf_val at x=0?

A pdf_val increases

B pdf_val decreases

C pdf_val stays the same

D pdf_val becomes zero

💡 Hint

Changing mean shifts the curve; check variable_tracker for mu and think how PDF at x=0 changes.

Concept Snapshot

Normal distribution uses mean (mu) and std dev (sigma).
Use scipy.stats.norm.pdf(x, mu, sigma) to get density at x.
PDF shows curve height, not direct probability.
Changing mu shifts curve; sigma changes spread.
Common for modeling natural data variations.

Full Transcript

This visual execution shows how to use scipy's normal distribution. First, we set mean and standard deviation. Then, we pick a point x to evaluate. Using norm.pdf, we get the density value at x. The tables track each variable's value step-by-step. Key moments clarify why mean and std dev matter and what PDF means. The quiz tests understanding of these steps and effects of changing parameters.