A Continuous Random Variable X Has the Probability Density Function $e ^ { - 2 x }$

question 52

Essay

A continuous random variable X has the probability density function f(x) = 2 $e ^ { - 2 x }$ , x $\ge$ 0.
a. Find the mean and standard deviation of X.
b. What is the probability that X is between 1 and 3?
c. What is the probability that X is at most 2?

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Definitions:

Classical Conditioning

An instructional process where pairing two stimuli repeatedly results in a response first prompted by the second stimulus, but eventually prompted by only the first stimulus.

Extinction

A process in which the conditioned response is weakened when the conditioned stimulus is repeated without the unconditioned stimulus.

Acquisition

The gradual formation of an association between conditioned and unconditioned stimuli.

Spontaneous Recovery

A process in which a previously extinguished response reemerges after the conditioned stimulus is presented again.