Question

please explain all steps

7. Suppose lightning strikes at an average of 1.4 strikes per minute during a particular storm. You play the following game: if the next strike occurs within the next minute, you win 3 dollars, if the next strike occurs between 1 minute and 2 minutes from now, you win 5 dollars, and if the next strike occurs more than 2 minutes from now, you win 1 dollar. How much should someone be charged to play this game, to make it a "fair game?" Ans: $3.25

Answer 1

here for exponential distribution parameter $\lambda$ =1.4

therefore P(next strike occur within next minute)=P(X<1)=1-e^-$\lambda$x =1-e^-1.4 =0.7534

P(next strike occur between 1 and 2 minute)=P(!<X<2)=(1-e^-1.4*2)-(1-e^-1.4*1)=0.1858

P(strike after 2 minutes)= e^-1.4*2 =0.0608

therefore expected value =fair price to be charges =3*0.7534+5*0.1858+1*0.0608=$ 3.25