There are three people racing T1T2T3Exponentialalpha are ide

There are three people racing, T1,T2,T3~Exponential(alpha) are identically distributed. Tmax means the time that all racers get into the finish line. What\'s Tmax?also, what is the expected value for Tmax?

Solution

Three people racing with exponential distribution T1, T2 and T3

T =max(T1, T2, T3)

F(T) = P(Max T1, T2, T3

P(T1

= (1-e^-alphaT)³/alpha³

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E(T) =1- integral 0 to infinity of F(T) dt

=1- integral 0 to infinity of F(T) dt

=1-(3-3/2+1/6)1/alpha^3

= 11/6 alpha^3