The Standard Deviation for a Random Variable with Probability Density $\sigma=\left[\int_{-\infty}^{\infty}(x-\mu)^{2} f(x) d x\right]^{1 / 2}$

Multiple Choice

The standard deviation for a random variable with probability density function f and mean µ is defined $\sigma=\left[\int_{-\infty}^{\infty}(x-\mu) ^{2} f(x) d x\right]^{1 / 2}$ . Find the standard deviation for an exponential density function with mean $10$ .

A) $10$
B) $2.5$
C) 2
D) $3.3$
E) 5