Is f(x) = $\left( \frac { 3 } { 2 } \right)$ x - 1 a probability density function for 0 ≤ x ≤ 2?

Name: Is f(x) = $\left( \frac { 3 } { 2 } \right)$ x - 1 a probability density function for 0 ≤ x ≤ 2?
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Question

Quizplus · Accepted Answer

For a function to be a probability density function (PDF) over a certain interval, the integral of the function over that interval must equal 1. The integral of $f(x) = \left( \frac { 3 } { 2 } \right) x - 1$ from 0 to 2 is not 1, thus it does not meet the criteria for a PDF.

Is F(x) = (32)\left( \frac { 3 } { 2 } \right)(23​)

Is F(x) = $\left( \frac { 3 } { 2 } \right)$