2 years ago

Anyone finna talk.....rllly bored rn

SAT

1 answer:

melisa1 [442]2 years ago

3 0

Answer:

Hello what are you doin rn?

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Based the density function of the observed outcome, the probability $P(x\leq \frac{1}{3} )$ is equal to 0.1388.

<h3>What is a density function?</h3>

A density function can be defined as a type of function which is used to represent the density of a continuous random variable that lies within a specific range.

Given the following density function:

$f(x)=\left \{ {{2(1-x),\;0 < x < 1} \atop {0,\; otherwise}} \right.$

Next, we would calculate $P(x\leq \frac{1}{3} )$ ;

$P(x\leq \frac{1}{3} )=\int\limits^\frac{1}{3} _0 {f(x)} \, dx \\\\P(x\leq \frac{1}{3} )=2 \int\limits^\frac{1}{3} _0 {(1-x)} \, dx \\\\P(x\leq \frac{1}{3} )=2|x-\frac{x^2}{2} |\limits^\frac{1}{3} _0\\\\P(x\leq \frac{1}{3} )=2[\frac{1}{3} -\frac{1}{2} (\frac{1}{3})^2]\\\\P(x\leq \frac{1}{3} )=2[\frac{1}{3} -\frac{1}{18}]\\\\P(x\leq \frac{1}{3} )=0.1388$

Read more on probability here: brainly.com/question/25870256

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