Answer :
The standard deviation, A = -1 is the expected amount paid to this company in one year.
What is standard deviation?
- The variability in your dataset is measured by its standard deviation.
- It reveals the average deviation between each result and the mean.
- A low standard deviation denotes that values are grouped closely to the mean, while a large standard deviation denotes that values are often spread widely from the mean.
The required payment random variable is given by
1000(x - 2 )
where x posses poison distribution with mean 1.
the expected value to be paid in the one year is given by
= 1000 ∑x=3 ( x - 2 ) e!/x!
= 1000 ( ∞∑ x= 0 ( x- 2 ) e⁻¹/x! - 2∑x = 0 ( x - 2 ) e⁻¹/x!
= 1000 ( A - B )
the expected value to be paid in the one year is given by
= 1000 ∑x=3 ( x - 2 ) e!/x!
= 1000 ( ∞∑ x= 0 ( x- 2 ) e⁻¹/x! - 2∑x = 0 ( x - 2 ) e⁻¹/x!
P ( K=x ) = e⁻¹/x!
so
∑ x=0 x p( k = x ) = ∞∑x = 0 x e⁻¹/x! = 1
and ∞∑x = 0 e⁻¹/x! = 1
∵ A = ∞∑X = 0 (x - 2 )e⁻¹/x!
A = 1 - 2 * 1
A = -1
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