Element X is a radioactive isotope such that every 14 years, its mass decreases by half. Given that the initial mass of a sample
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Answer:
(a) The value of P (X = 7) is 0.1388.
(b) The value of P (X ≥ 3) is 0.9380.
(c) The value of P (2 < X < 7) is 0.5433.
(d)
(e)
Step-by-step explanation:
Let <em>X</em> = number of uranium fission tracks on per cm² surface area of the mineral.
The average number of track per cm² surface area is, <em>λ</em> = 6.
The random variable <em>X</em> follows a Poisson distribution with parameter <em>λ</em> = 6.
The probability mass function of a Poisson distribution is:
(a)
Compute the value of P (X = 7) as follows:
Thus, the value of P (X = 7) is 0.1388.
(b)
Compute the value of P (X ≥ 3) as follows:
P (X ≥ 3) = 1 - P (X < 3)
= 1 - P (X = 0) - P (X = 1) - P (X = 2)
Thus, the value of P (X ≥ 3) is 0.9380.
(c)
Compute the value of P (2 < X < 7) as follows:
P (2 < X < 7) = P (X = 3) + P (X = 4) + P (X = 5) + P (X = 6)
Thus, the value of P (2 < X < 7) is 0.5433.
(d)
The mean of the Poisson distribution is:
(e)
The standard deviation of the Poisson distribution is: