Practice Additive Property (19.X.2.2) - Poisson Distribution - Mathematics - iii (Differential Calculus)

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6 sample questions

Question 1.
If $X \sim Poisson(2)$ and $Y \sim Poisson(3)$ , what is the distribution of $X + Y$ ?
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Add the means.
Question 2.
Is the sum of two independent Poisson distributions Normal?
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Think about the independence and definition.
3Question 3.
If $X_1$ and $X_2$ are independent Poisson variables, what type is $X_1 + X_2$ ?
- Normal
- Poisson
- Uniform
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Reflect on the key properties of Poisson distributions.
4Question 4.
The means of two independent Poisson distributions combine to a different type of distribution.
- True
- False
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Think about how additive properties work.
Question 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?
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Just sum all individual means.
Question 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?
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Remember to treat each defect source independently.

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