Email, Theft Probability Analysis

62 a Received exactly 1 email 63 a 4 thefts occur in a minute

Mean = 2 Mean = 3.1

X = 1 X = 4

P(1) = P(4) =

b Received 5 or more email b No thefts

Mean = 2 Mean = 3.1

X ≥ 5 X = 0

P(0) = P(0) =

P(1) = c At least one theft

P(x < 1 ) = 0,0451 P(2) =

P(x ≥ 1) = 1 - 0,0451 P(3) =

P(4) = P(x < 5) = 0,9474

P(X ≥ 5) = 1 - 0,9474 = 0,0526 c Did not receive any emails

P(0) =

2¹ × 𝑒⁻²

1! = 0,2707

2⁰ × 𝑒⁻²

0! = 0,1353 2¹ × 𝑒⁻²

1! = 0,2707 2² × 𝑒⁻²

2! = 0,2707 2³ × 𝑒⁻²

3! = 0,1805 2⁴ × 𝑒⁻²

4! = 0,0902

2⁰ × 𝑒⁻²

0! = 0,1353

3

4 thefts occur in a minute

=0,9549 3,1⁴ × 𝑒^−3,1

4! = 0,1734

3,1⁰ × 𝑒^−3,1

0! = 0,0451