Answer to Question #119228 in Statistics and Probability for Stat 2

Question

5.A baseball team has scheduled its opening game for April 5. It is assume that if it snows on April 5, the game is postponed and will be play on the next day that it
does not snow. The team purchased insurance against snow. The policy will pay $1,000 for each day, up to 2 days that the game is postponed. It is determined that
the number of consecutive days of snow beginning on April 1, is a Poisson random variable with mean 0.6. What is the expected cost to the nearest one dollar that
the insurance company will have to pay?

6. The mean number of errors due to a bug occurring in a minute is 0.0001. What is the probability that no error will occur in 20 minutes?

7. Suppose that at a busy traffic junction, the probability p of an individual car having an accident is 0.0001. During a certain part of the day, 100 cars pass through the
junction. What is the probability of two or more cars being involved in an accident within this period?

Answer 1

5) Y - amount we need to pay

P(X=0)=P(Y=0)=e^-0.6=0.5488

P(X=1)=P(Y=1000)=0.6e^-0.6=0.3293

P(X≥2)=P(Y=2000)=1-1.6e^-0.6=0.1219

expected cost:EY=0*0.5488+1000*0.3293+2000*0.1219=573 $

6)λ=0.0001 per minure or λ=0.002 in 20 minutes

P(0)=e^-0.002=0.998

7)λ=np=100*0.0001=0.01

P(x≥2)=1-P(x=0)-P(x=1)=1-e^-0.01-0.01e^-0.01=1-0.99-0.0099=0.0001