Answer:

Step-by-step explanation:

If the STANDARD deviation of a Poisson VARIABLE is 2, what is P (x greater than 1.5 and less than 2.9)?

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3 Answers

B.L. Srivastava

B.L. Srivastava, M.Sc.Ph.D. Mathematics, Chhatrapati Shahu JI Maharaj University

Updated Mar 4 · Author has 2.6k answers and 460.9k answer views

A Poisson variate X is distributed according to the formula ;

P(X = x) = e(-m)m^(x)/x! ; x = 0, 1, 2, 3 …, . and m is parameter . We know that mean m of distribution = (s.d.)^2 = 4 (given). Now, we are required to find, P(1.5 < X < 2.9). Since Poisson distribution is a discrete distribution, therefore it takes discrete values 0, 1, 2, … .. .. Therefore,

1.5 < X < 2.9 means X takes value 2 . HENCE P(1.5 < X < 2.9) = P(X = 2) = e^(-4)(4)^(2)/2! = 8/e^(4) .