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8.02 Probability density functions

Interactive practice questions

Consider the probability density function $p\left(x\right)$p(x) drawn below for a random variable $X$X.

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a

Calculate the area between $p(x)$p(x) and the $x$x axis.

b

Which feature(s) of $p\left(x\right)$p(x) is also a feature of all probability distribution functions? Select all options that apply.

$p\left(x\right)$p(x) is positive for all values of $x$x.

A

$p\left(x\right)$p(x) is defined in the region $-\infty<x<.

B

$p\left(x\right)$p(x) is only defined in the region $10\le x\le80$10x80.

C

The area under $p\left(x\right)$p(x) is equal to $1$1.

D
c

Calculate $P$P$($($X$X$\le$$54$54$)$) using geometric reasoning.

d

Calculate $P$P$($($X$X$>$>$34$34$)$) using geometric reasoning.

e

Calculate $P$P$($($44$44$<$<$X$X$\le$$53$53$)$) using geometric reasoning.

f

Calculate $P$P$($($X$X$\le$$56$56$\mid$$X\ge44$X44$)$) using geometric reasoning.

Easy
8min

Consider the probability density function $p\left(x\right)=\frac{1}{40}$p(x)=140 for $60\le x\le100$60x100 and $p\left(x\right)=0$p(x)=0 otherwise.

Easy
6min

Consider the probability density function $p\left(x\right)$p(x) drawn below for a random variable $X$X.

Easy
9min

Consider the probability density function $p\left(x\right)$p(x) drawn below for a random variable $X$X.

Easy
7min
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Outcomes

ACMMM165

understand the concepts of a probability density function, cumulative distribution function, and probabilities associated with a continuous random variable given by integrals; examine simple types of continuous random variables and use them in appropriate contexts

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