19.X.2.2. Additive Property

Try these first

1. 1.

   If $X \sim Poisson(2)$ and $Y \sim Poisson(3)$, what is the distribution of $X + Y$?

   Hint

   Add the means.

2. 2.

   Is the sum of two independent Poisson distributions Normal?

   Hint

   Think about the independence and definition.

3. 3.

   If $X_1$ and $X_2$ are independent Poisson variables, what type is $X_1 + X_2$?

   • Normal
   • Poisson
   • Uniform

   Hint

   Reflect on the key properties of Poisson distributions.

4. 4.

   The means of two independent Poisson distributions combine to a different type of distribution.

   • True
   • False

   Hint

   Think about how additive properties work.

5. 5.

   In a service station, cars arrive following Poisson distributions: $A \sim Poisson(5)$, $B \sim Poisson(7)$, and $C \sim Poisson(4)$. What is the mean of total cars arriving?

   Hint

   Just sum all individual means.

6. 6.

   A factory has three machinery lines producing defects with averages 2, 3, and 1: $X \sim Poisson(2)$, $Y \sim Poisson(3)$, $Z \sim Poisson(1)$. What is the distribution of total defects?

   Hint

   Remember to treat each defect source independently.