Given an exponential distribution with =28, what is the probability that the arr

ID: 3339105 • Letter: G

Question

Given an exponential distribution with =28, what is the probability that the arrival time is

less than X = 0.1?

greater than 0.1?

BETWEEN x = 0.1 AND x = 0.3

a. P(Arrival timeless than<0.1)equals=

(Round to four decimal places as needed.)

b. P(Arrival timegreater than>0.1)=

(Round to four decimal places as needed.)

P(0.1less than<Arrival timeless than<0.3) =

(Round to four decimal places as needed.)

d. P(Arrival timeless than<0.1 or arrival timegreater than>0.3 =

(Round to four decimal places as needed.)

less than X = 0.1?

greater than 0.1?

BETWEEN x = 0.1 AND x = 0.3

LESS THAN x= 0.1 OR GREATER THAN x=0.3

= 28

P(X < x) = 1 - e-x

P(X > x) = e-x

a) P(X < 0.1) = 1 - e-28*0.1 = 0.9392

b) P(X > 0.1) = e-28*0.1 = 0.0608

c) P(0.1 < X < 0.3) = P(X < 0.3) - P(X < 0.1)

= (1 - e-28*0.3 ) - (1 - e-28*0.1 )

= 0.0606

d) P(X < 0.1 or X > 0.3) = 1 - P(0.1 < X < 0.3) = 1 - 0.0606 = 0.9394

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.