Question

Suppose that the US government receives on average 1.4 requests for political asylum per day. What is P[X = 0] ,P[X=1] , P[X=2] ,and P[X=3], the E[X] and variance? Does the sum of these probabilities equal 1? Explain.

Answer 1

Solution :

Given that ,

mean = = 1.4

Using poisson probability formula,

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

(a)

P(X = 0) = (e^-1.4 * 1.4⁰⁾ / 0! = 0.2466

(b)

P(X = 1) = (e^-1.4 * 1.4¹⁾ / 1! = 0.34524

(c)

P(X = 2) = (e^-1.4 * 1.4²⁾ / 2! = 0.24167

(d)

P(X = 3) = (e^-1.4 * 1.4³) / 3! = 0.11278

(e)

E(X) = 1.4

Variance = 1.4

The sum of these probabilities is not equal to 1 .