The Standard Deviation for a Random Variable with Probability Density $f$

question 123

Multiple Choice

The standard deviation for a random variable with probability density function $f$ and mean $\mu$ 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
• C) 5
• D) \(3.3\)
• E) \(2.5\)

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