Question

Suppose X has a Poisson distribution with a mean of 1.5. Determine the following probabilities. Round your answers to four decimal places (e.g. 98.7654).

(a)P(X = 1)
(b)P(X ≤ 3)
(c)P(X = 7)
(d)P(X = 2)

Answer 1

Solution :

Given that ,

mean = = 1.5

Using poisson probability formula,

P(X = x) = (e^- * ^x ) / x!

a) P(X = 1)

P(X = 1) = (e^-1.5 * 1.5¹ / 1! )

P(X = 1) = 0.3347

Probability = 0.3347

b) P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= (e^-1.5 * 1.5⁰ / 0! ) + (e^-1.5 * 1.51/ 1! ) + (e^-1.5 * 1.5² / 2! ) + (e^-1.5 * 1.5³ / 3! )

= 0.2231 + 0.3347 + 0.251 + 0.1255

= 0.9344

Probability = 0.9344

c) P(X = 7) =  (e^-1.5 * 1.5⁷ / 7! )

= 0.00000005

Probability = 0.0000005

d) P(X = 2) =  (e^-1.5 * 1.5² / 2! )

= 0.2510

Probability = 0.2510