Answer:
a) 20 second
b) 20 second
c) 1 minute
Step-by-step explanation:
Let X be the exponential random variable arising from the Poisson process with the rate λ = 3 counts per minute. Its cdf is then given by:
F(x) = I - e^-3x, x >= 0
Calculate the mean and the standard deviation of the random variable X as follows:
Е(X) =I/λ =I/3=20 second
std (x) =√1/λ^2=1/3=20 second
For the part c), write down the equation:
0.95 = P(X < x) = F(x) = I - e^-3x
and solve the equation for x to obtain:
x = -1/3 In 0.05 = 0.9985 ≅ 1 minute