We are required to find the standard deviation of the exponential distribution.
The standard deviation of the <em>exponential</em> distribution whose density function is f(x)=10*e^(-10x) is 0.1.
By convention, exponential probability distributions have density function in the form:
f(X) = f(x)=μ*e^(-μx)............... equation 1.
Where μ = decay parameter.
However, the <em>decay parameter</em> is related to the standard deviation of the distribution by the formular:
μ = 1/m
Where m = Standard deviation of the distribution.
Therefore, by comparison of equation 1 with f(x)=10*e^(-10x).
It is evident that the decay parameter, μ = 10
Therefore, the standard deviation, m = 1/μ = 1/10 = 0.1.
The standard deviation of the exponential distribution whose density function is f(x)=10*e^(-10x) is 0.1
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