Let X be a geometries random variable with p 08 Compute the

Let X be a geometries random variable with p= 0.8. Compute the probabilities of the following events: X > 3 4 X 7 or X > 9

Solution

a)

Note that the cumulative distribution function of a geometric variable is

F(x) = 1 - (1-p)^x

Here,

P(X>3) = 1 - P(x<=3)

= 1 - (1 - (1-0.8)^3)

= 0.008 [ANSWER]

***************

b)

P(4<=x<=7 or x >9) = F(7) - F(3) + (1-F(9))

= (1-(1-0.8)^7) - (1-(1-0.8)^3) + (1-(1-(1-0.8)^9))

= 0.007987712 [ANSWER]