28.3.1. Uniform Distribution

Try these first

1. 1.

   Define uniform distribution in your own words.

   Hint

   Think about rolling dice or drawing cards.

2. 2.

   What is the probability of picking any number between 2 and 5 from a uniform distribution defined from 1 to 10?

   Hint

   Calculate the area of the segment over the total area.

3. 3.

   What does uniform distribution imply?

   • All outcomes are equally likely
   • Only one outcome is likely
   • Some outcomes are impossible

   Hint

   Think about a fair game like dice where each face is equally likely.

4. 4.

   True or False: In uniform distribution, the probability density function is non-constant.

   • True
   • False

   Hint

   Remember the shape of the PDF graph.

5. 5.

   A structural engineer must calculate the load on a beam that is assumed to be uniformly distributed between 500 lbs and 1000 lbs. What is the expected load on the beam?

   Hint

   Use the expected value formula.

6. 6.

   If a truck load is uniformly distributed between 0 and 2000 kg, how would you confirm if this assumption is valid given real-world data?

   Hint

   Consider using statistical software for data visualization.