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

question 50

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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Definitions:

Integration Phase

The integration phase is a stage in various processes (psychological therapy, project development) where different elements or experiences are combined and fully assimilated.

Presynaptic Neuron

The neuron that sends a signal across the synaptic gap to another neuron during neurotransmission.

Reuptake

The process by which neurotransmitters are taken back into the neuron after being released into the synapse, effectively stopping their action on adjacent neurons.

Neurotransmitters

Chemical substances that carry signals from one neuron to another.