sympy.stats.Logarithmic() in Python

In sympy.stats, the Logarithmic class represents the logarithmic distribution, a discrete probability distribution which is parameterized by a single parameter p, where 0<p<1. The logarithmic distribution is often used in various probabilistic models and is sometimes referred to as the logarithmic series distribution.

Here's how you can use the Logarithmic class in sympy.stats:

1. Define a random variable with a logarithmic distribution.
2. Compute various properties of the distribution like density, expectation, variance, etc.

Here's a simple example:

from sympy.stats import Logarithmic, density, E, variance from sympy import Symbol p = Symbol('p', positive=True, real=True) # Parameter of the distribution Z = Logarithmic('Z', p) # Define a random variable with a logarithmic distribution # Compute the probability mass function (PMF) pmf = density(Z).dict # Compute the expectation and variance expectation = E(Z) var = variance(Z) # Print the results print("PMF:", pmf) print("Expectation:", expectation) print("Variance:", var) 

In this example, we've defined a random variable Z with a logarithmic distribution. We then computed and printed its PMF, expectation, and variance. Note that the results are in symbolic form because the distribution's parameter p is symbolic. If you have a specific value of p, you can substitute it in to get numerical results.

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