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Answer:
Step-by-step explanation:
The model , the number of planets found up to time
, as a Poisson process. So, the
has distribution of Poison distribution with parameter
a)
The mean for a month is, per month
(Here. t = 24)
For Poisson process mean and variance are same,
(Poisson distribution mean and variance equal)
The standard deviation of the number of planets is,
b)
For the Poisson process the intervals between events(finding a new planet) have independent exponential distribution with parameter . The sum of
of these independent exponential has distribution Gamma
.
From the given information, and
Calculate the expected value.
(Here, and
)
C)
Calculate the probability that she will become eligible for the prize within one year.
Here, 1 year is equal to 12 months.
P(X ≤ 12) = (1/Г (k)λ^k)(x)^(k-1).(e)^(-x/λ)
Hence, the required probability is 0.2149 or 21.49%