Exponential Distribution Formula
The exponential distribution formula is used to find the exponential distribution of a function. Exponential distribution refers to the process in which the event happens at a constant average rate independently and continuously. The exponential distribution is most often known as the memoryless distribution because it means that past information has no effect on future probabilities. Let us learn the exponential distribution formula with a few solved examples.
What is the Exponential Distribution Formula?
The exponential distribution formula is the formula to define the exponential distribution. For exponential distribution, the variable must be continuous and independent. The exponential distribution formula is given by:
f(x) = me-mx
or
f(x) = (1/μ) e-(1/μ)x
Where:
- m = the rate parameter or decay parameter.
- μ = average time between occurrences.
Let's have a look at solved examples to understand the exponential distribution formula better.
Solved Examples on Exponential Distribution Formula
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Example 1: A postal clerk spends an average of 4 minutes with their customer. The time has exponential distribution. Find the value of the function at x = 5 by using the exponential function formula.
Solution:
Given μ = 4, hence m = 1/μ = 1/4 = 0.25
f(x) = me-mx
f(x) = 0.25 e(-0.25)5
f(x) = 0.072
Answer: The value of the function at x = 5 is 0.072 -
Example 2: A person spends an average of 10 minutes on a counter. The time has exponential distribution. Find the value of the function at x = 7 by using the exponential function formula.
Solution:
Given μ = 10, hence m = 1/μ = 1/10 = 0.1
f(x) = me-mx
f(x) = 0.1 e(-0.1)7
f(x) = 0.04966
Answer: The value of the function at x = 7 is 0.04966
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