This calculator computes probabilities for the lognormal distribution using the mean (π), standard deviation (π), and a random variable value (π₯). It also visualizes the distribution and highlights the cumulative probability \( P(X \leq x) \).

**P(X = ):**

**P(X < ):**

**P(X β€ ):**

**P(X > ):**

**P(X β₯ ):**

## Understanding the Lognormal Distribution

The **Lognormal Distribution** is a continuous probability distribution of a random variable whose logarithm is normally distributed. It is widely used in fields like finance, reliability analysis, and biological modeling.

In particular, the Black-Scholes Model assumes that the price of financial assets follows a lognormal distribution, which allows it to model stock prices effectively over time.

### Key Components of the Lognormal Distribution

**Mean (π):**The mean of the underlying normal distribution.**Standard Deviation (π):**The standard deviation of the underlying normal distribution.**Random Variable (π₯):**The value for which probabilities are being calculated.

### Formula for Lognormal Distribution

The probability density function (PDF) for the lognormal distribution is:

### Example Calculation

Let's assume the mean is \( \mu = 0 \), the standard deviation is \( \sigma = 1 \), and we want to find the probability for \( x = 1 \).

### Further Reading

Suf is a senior advisor in data science with deep expertise in Natural Language Processing, Complex Networks, and Anomaly Detection. Formerly a postdoctoral research fellow, he applied advanced physics techniques to tackle real-world, data-heavy industry challenges. Before that, he was a particle physicist at the ATLAS Experiment of the Large Hadron Collider. Now, heβs focused on bringing more fun and curiosity to the world of science and research online.