A system consisting of one original unit plus a spare can function for a random amount of time X. If the density of Xis given (in units of months) byf(x) ={cxe -x/2 x>0 0 x<0 What is the probability that the system functions for at least 5 months?

0.2397

Step-by-step explanation:

Given data:

fX(x) = Cxe^(−x/2) if x >0 0 otherwise, where C > 0 is some constant.

The probability that the system functions for at least 5 months

= 0.2397

attached below is a detailed solution

Triangle BDC is an isosceles. 
So, angle DBC = angle DCB.

180° - 100° =80°
80÷2=40.

Angle C = 40°

Angle ABD is half angle DBC, so <ABD = 40°÷2=20° 
Therefore, angle ABC=20°+40°=60°
To get the angle A, use the angles in a triangle ABC.

180° - (60°+40°)=80°

Angle A = 80°