How do you draw the graph of a continuous uniform distribution?

Conditions

• You know the values of the lower bound a and the upper bound b.
• You have calculated the constant probability density value $\frac{1}{b-a}$.

Reasoning, step by step

1. Mark the lower bound a and the upper bound b on the x-axis.
2. Calculate the probability density function value using the formula $f(x) = \frac{1}{b-a}$.
3. Mark this constant density value on the y-axis.
4. Draw a rectangle spanning from a to b on the x-axis with a height equal to the density value.

Example

For the bus waiting time example, the narrator marks 0 and 60 on the x-axis, and $\frac{1}{60}$ on the y-axis, then draws a rectangle filling the space between them to visually confirm the constant probability density over the 60-minute interval.

Common misconceptions

• Drawing a curve instead of a rectangle.
• Forgetting to connect the top of the rectangle to the y-axis value, leaving the height ambiguous.

Watch the explanation

Explore next

• What is the probability density function formula for a continuous uniform distribution on the interval [a, b]?
• How do you calculate the probability of an event occurring in a subinterval for a continuous uniform distribution?
• Why does a uniform distribution always have a rectangular graph?