Solution Found!
Solution: The random variable X follows a Poisson process
Chapter 6, Problem 10E(choose chapter or problem)
Problem 10E
The random variable X follows a Poisson process with the given value of λ and t.
Assuming λ = 0.02 and t = 50, compute
(a) P(2)
(b) P(X<2)
(c) P(X ≥ 2)
(d) P(1 ≤ X ≤ 3)
(e) μX and σX
Questions & Answers
QUESTION:
Problem 10E
The random variable X follows a Poisson process with the given value of λ and t.
Assuming λ = 0.02 and t = 50, compute
(a) P(2)
(b) P(X<2)
(c) P(X ≥ 2)
(d) P(1 ≤ X ≤ 3)
(e) μX and σX
ANSWER:
Answer
Step 1 of 5
(a)
The random variable X follows a Poisson process with the given value of λ and t.
Assuming λ = 0.02 and t = 50, we are asked to compute
If X is the number of successes in an interval of fixed length t, then the probability
of obtaining x successes in the interval is
…………(1)
We have given λ = 0.02, t = 50 and
Using equation (1), we can write that,
Hence is