That expression is the expected value of your winnings, or "the average amount you will win (or lose) per game in the long run".
I think it's less than 7/2 usually bigger numbers are less in this case.
sorry if you got that wrong but i'm 85% sure
Answer:
0.36427
Step-by-step explanation:
Mean = λ = 18 messages per hour
P(X = x) = (e^-λ)(λ⁻ˣ)/x!
P(X ≤ x) = Σ (e^-λ)(λ⁻ˣ)/x! (Summation From 0 to x)
But the probability required is that the messages thay come in an hour is between 15 and 20, that is, P(15 < X < 20)
P(15 < X < 20) = P(X < 20) - P(X ≤ 15)
These probabilities will be evaluated using a cumulative frequency calculator.
P(X < 20) = 0.65092
P(X ≤ 15) = poissoncdf(18, 15) = 0.28665
P(15 < X < 20) = P(X < 20) - P(X ≤ 15) = 0.65092 - 0.28665 = 0.36427.
You can use the Poisson distribution calculator here
https://stattrek.com/online-calculator/poisson.aspx
Yes, they are independent. First of all, we know that P(A) = 1/4, P(B) = 2/5, and P(A and B) = 1/10. To know if two events are independent, the following questions must be true: P(A)*P(B) = P(A and B). So since (1/4)*(2/5) = 2/20 which equals 1/10, these events are independent
