At the airport, there are three counters for checking the luggage. The employees at each counter work independently with the time for each customer modeled as an exponential distribution. The average time is one minute for one counter, two for the next, and three minutes for the third. An actuary, who is next in line, will take the next available counter, i. e. the minimum of the three. What is the variance of the actuary's wait time

is only a line? i think so

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.