Question

Suppose that X is an exponentially distributed random variable with λ = 0.37

Find each of the following probabilities:

A. P(X > 1)

B. P(X > 0.29)

C. P(X < 0.37)

D. P(0.31 < X < 2.04)

Answer 1

We know that the P(X<=x)= 1- e^-lambda*x

Lambda= 0.37

Thus,

A.

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

= 1- (1-e^-0.37*1)

= e^-0.37

= 0.69073

B.

P(X>0.29)= 1-P(X<=0.29)

= 1- (1-e^-0.37*0.29)

= e^-0.1073

= 0.8982562

C.

P(X<0.37)

= 1-e^-0.37*0.37

=1- e^-0.1369

= 1-0.8720574
= 0.1279426

D.

P(0.31 < X < 2.04)

= P(X<2.04) - P(X<0.31)

=  (1-e^-0.37*2.04 ) -  (1-e^-0.37*0.31)

= -e^-0.37*2.04 + e^-0.37*0.31

= -e^-0.7548 + e^-0.1147

= - 0.4701046 +0.8916336

= 0.421529