Suppose That the Random Variable X Has an Exponential Distribution $x$

question 12

Essay

Suppose that the random variable x has an exponential distribution with θ = 3. a. Find the probability that $x$ assumes a value more than three standard deviations from $\mu$ .
b. Find the probability that $x$ assumes a value less than one standard deviation from $\mu$ .
c. Find the probability that $x$ assumes a value within a half standard deviation of $\mu$ .

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Definitions:

Millimeters

A unit of length in the metric system, equal to one thousandth of a meter, used to measure small distances.

Focal Plane

The specific distance at which the lens of a camera or microscope focuses light to form a sharp image.

Depth of Field

The range of distance within a photograph that appears acceptably sharp, influenced by the aperture, focal length, and distance from the subject.

Resolution

The process of reducing or separating something into its components or the clarity and detail of an image.