Probability density and cumulative functions in SciPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a Probability Density Function (PDF)?

A PDF shows how likely it is to find a value near a specific point in a continuous distribution. The area under the PDF curve between two points gives the probability of the value falling in that range.

beginner

What does the Cumulative Distribution Function (CDF) represent?

The CDF gives the probability that a random variable is less than or equal to a certain value. It is the area under the PDF curve from the smallest value up to that point.

intermediate

How do you calculate the PDF and CDF using scipy for a normal distribution?

Use scipy.stats.norm. For PDF: norm.pdf(x, loc=mean, scale=std). For CDF: norm.cdf(x, loc=mean, scale=std). Replace x with the value, mean and std with distribution parameters.

beginner

Why is the area under the PDF curve always equal to 1?

Because the total probability of all possible outcomes must be 1. The PDF curve represents how this total probability is spread over values.

intermediate

What is the relationship between PDF and CDF?

The CDF is the integral (sum) of the PDF from the lowest value up to a point. The PDF is the derivative (rate of change) of the CDF.

What does the CDF value at x represent?

A Probability that the variable is exactly x

B Mean of the distribution

C Probability density at x

D Probability that the variable is less than or equal to x

The CDF gives the probability that the variable is less than or equal to x.

Which scipy function calculates the PDF of a normal distribution?

A norm.cdf()

B norm.mean()

C norm.pdf()

D norm.var()

norm.pdf() calculates the probability density function values.

What is the total area under a PDF curve?

A 0

B 1

C Depends on the distribution

D Infinity

The total area under the PDF curve is always 1, representing total probability.

If PDF is the derivative of CDF, what is CDF in terms of PDF?

A Integral of PDF

B Derivative of PDF

C Square of PDF

D Logarithm of PDF

CDF is the integral (area under curve) of the PDF.

Which of these is true for a continuous random variable?

A Probability at a single point is zero

B Probability at a single point is one

C PDF values are probabilities

D CDF decreases as x increases

For continuous variables, probability at an exact point is zero; probabilities come from intervals.

Explain the difference between Probability Density Function (PDF) and Cumulative Distribution Function (CDF).

Think about how probability is spread and accumulated.

Describe how to use scipy to find PDF and CDF values for a normal distribution at a given point.

Recall the function names and parameters.