Interactive practice questions
Consider the probability density function $p$p where $p\left(x\right)=\frac{1}{20}$p(x)=120 when $25\le x\le45$25≤x≤45 and $p\left(x\right)=0$p(x)=0 otherwise.
Use integration to determine the expected value of $p\left(x\right)$p(x).
Use integration to determine the variance of $p\left(x\right)$p(x).
Round your answer to two decimal places if necessary
Consider the probability density function $p$p, where $p\left(x\right)>0$p(x)>0 when $4\le x\le12$4≤x≤12 and $p\left(x\right)=0$p(x)=0 otherwise.
The graph of $y=p\left(x\right)$y=p(x) is shown below.
The probability density function of a random variable $X$X is drawn below. Its non-zero values lie in the region $0\le x\le k$0≤x≤k.
Consider the probability density function $p$p, where $p\left(x\right)=\frac{1}{18}\left(x+1\right)$p(x)=118(x+1) when $-1\le x\le5$−1≤x≤5 and $p\left(x\right)=0$p(x)=0 otherwise.