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

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The Answer of 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

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

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