A random variable X is said to follow exponential distribution if it follows the following probability mass function.

Exponential probability distribution is a continuous distribution.

**Probability Distribution Function of Exponentially Distributed Variable X**

**Probability Distribution Function of Exponentially Distributed Variable X**

It is heavily used in the Internet traffic modelling and of study queuing models.

Numerical Example-

**Problem-**

If a computer receives a packet in its interface queue with average 5 milliseconds. Find out that a packet will not wait for more than 15 millisecond.

**Solution-**

Calculate it yourself

**Mean or Expectation of Exponential Distributed Variable X**

**Mean or Expectation of Exponential Distributed Variable X**

**Variance of Exponential Distributed Variable X**

**Variance of Exponential Distributed Variable X**

**Python Code for Exponential Distribution**

**Python Code for Exponential Distribution**

**import numpy as np**

**import matplotlib.pyplot as plt**

**#mean=1/lambda**

**mean1=0.10**

**mean2=0.50**

**y1 = np.random.exponential(mean1, 5000)**

**y2 = np.random.exponential(mean2, 5000)**

**plt.subplot(2,2,1)**

**plt.title(“mean=0.10”)**

**plt.hist(y1, density=True, bins=500,lw=0,alpha=0.5)**

**plt.subplot(2,2,2)**

**plt.title(“mean=0.50”)**

**plt.hist(y2, density=True, bins=500,lw=0,alpha=0.6)**

**plt.savefig(“ExponentialDistribution.png”)**

Output of the program would be

**Conclusion**

In thisĀ post, I have explained about exponential distribution. Hope you will understand and apply.

**References-**

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