A Continuous Random Variable X Has the Probability Density Function

question 74

Essay

A continuous random variable X has the probability density function f(x) = 2e-2x, x  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:

Ligand-Gated

Referring to ion channels that open in response to the binding of a chemical messenger (ligand), such as a neurotransmitter.

Acetylcholine

A neurotransmitter involved in many functions including muscle movement, heart rate, and the modulation of brain activity.

GABA

Gamma-Aminobutyric Acid, an inhibitory neurotransmitter in the central nervous system that plays a key role in reducing neuronal excitability throughout the nervous system.

Receptor Downregulation

A decrease in the number of receptors on the surface of target cells, often in response to high levels of a hormone or neurotransmitter.