Respuesta :
Answer:
The answers are;
a. The probability of more than one death in a corps in a year is 0.12521.
b. The probability of no deaths in a corps over five years is 4.736 × 10⁻².
Step-by-step explanation:
For Poisson Distribution we have
Pₓ(k) = [tex]\frac{(\lambda t)^k e^{-(\lambda t)} }{k!}[/tex]
Where:
λ = Mean per unit time
k = Specified data point
t = time
e = Euler constant
a. The probability of more than one death in a corps in a year is given by
The mean of the Poisson distribution for one year is given as
λ·t = 0.61 × 1 = 0.61
Therefore by using complement principle, we have
P (X >1) = 1 - P(X = 0) - - P(X = 1)
=1- [tex]\frac{(0.61)^0 e^{-(0.61)} }{0!}[/tex] - [tex]\frac{(0.61)^1 e^{-(0.61)} }{1!}[/tex]
= 1 - 0.543 - 0.3314
= 0.12521
b. Here we have t = 5
Therefore the mean = λ·t = 0.61×5 = 3.05
The probability of there being no deaths in a corps for over five years is
P (X =0) = [tex]\frac{(3.05)^0 e^{-(3.05)} }{0!}[/tex] = 4.736 × 10⁻²
The probability is 4.736 × 10⁻² .
Answer:
A) 0.1252
B) 0.0474
Step-by-step explanation:
A) First of all let's call the number of soldiers killed by horse kicks each year "X"
Thus, T = 1 and so X will have a Poisson distribution of;
Mean EX = λT = 0.61 x 1 = 0.61
Thus, the probability of more than one death in a corps in a year is given as;
P(X>1) = 1 - P( X = 0) - P(X=1)
= 1 - e^(-0.61)(0.61^(0)/0!) - e^(-0.61)(0.61^(1)/1!)
= 1 - 0.5434 - 0.3314 = 0.1252
B) let X1 represent the number of soldiers killed by horse kicks in 5 years.
Thus, T = 5 and so X1 will have a Poisson distribution of;
Mean EX1 = λT = 0.61 x 5 = 3.05
probability of no deaths in a corps over five years is given as;
P(X=0) = e^(-3.05)(3.05^(0)/0!)
= 0.0474
