If the standard deviation of a Poisson variateX is 2what is p (1.5lessthan X and more than 2.9)?
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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) .