Question

Suppose that random variable

X
X
is uniformly distributed between 5 and 22. Draw a graph of the density function, and then use it to help find the following probabilities:

Answer 1

The density function is just the piecewise function,


`f_X(x)=\begin{cases}\frac1{22-5}=\frac1{17}&\text{for }5\le x\le22\\0&\text{otherwise}\end{cases}`

i.e. a rectangle of height
`\frac1{17}` and length 17 plotted over the interval
`[5,22]`. Any probabilities that you need to find are then areas of smaller rectangles.