Interactive practice questions
Consider the probability density function $p\left(x\right)$p(x) drawn below for a random variable $X$X.
Calculate the area between $p(x)$p(x) and the $x$x axis.
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.
$p\left(x\right)$p(x) is defined in the region $-\infty
$p\left(x\right)$p(x) is only defined in the region $10\le x\le80$10≤x≤80.
The area under $p\left(x\right)$p(x) is equal to $1$1.
Calculate $P$P$($($X$X$\le$≤$54$54$)$) using geometric reasoning.
Calculate $P$P$($($X$X$>$>$34$34$)$) using geometric reasoning.
Calculate $P$P$($($44$44$<$<$X$X$\le$≤$53$53$)$) using geometric reasoning.
Calculate $P$P$($($X$X$\le$≤$56$56$\mid$∣$X\ge44$X≥44$)$) using geometric reasoning.
Consider the probability density function $p\left(x\right)$p(x) drawn below for a random variable $X$X.
Consider the probability density function $p\left(x\right)=\frac{1}{40}$p(x)=140 for $60\le x\le100$60≤x≤100 and $p\left(x\right)=0$p(x)=0 otherwise.
Consider the probability density function $p\left(x\right)=\frac{5}{17}$p(x)=517 for $1.2\le x\le4.6$1.2≤x≤4.6 and $p\left(x\right)=0$p(x)=0 otherwise.