Interactive practice questions
A uniform probability density function, $P\left(x\right)$P(x), is positive over the domain $\left[20,50\right]$[20,50] and $0$0 elsewhere.
State the function defining this distribution.
| $P\left(x\right)$P(x) | $=$= |  |
$\editable{}$ | if $\editable{}\le x\le\editable{}$≤x≤ | ||
| $\editable{}$ | for all other values of $x$x |
Use integration to determine the expected value of the distribution.
Use integration to determine the variance $V\left(X\right)$V(X) of the distribution.
The distribution is transformed to the random variable $Y$Y by $Y=2X+4$Y=2X+4. Calculate $E\left(Y\right)$E(Y), the expected value of $Y$Y.
Determine the variance $V\left(Y\right)$V(Y) of the random variable $Y$Y as defined by $Y=2X+4$Y=2X+4.
Determine the standard deviation $SD\left(Y\right)$SD(Y) of $Y$Y.
Round your answer to one decimal place.
A continuous random variable $X$X has a uniform probability density function over the domain $\left[10,80\right]$[10,80].
$X$X is transformed to the random variable $Y$Y by $Y=2X+3$Y=2X+3.
Consider the graph of the probability density function $P\left(x\right)$P(x) shown.
Consider the graph of the probability density function $P\left(x\right)$P(x) shown.