Answer to Question #115114 in Statistics and Probability for Mariamyussifsaeed

Question

A5. A baseball team has scheduled its opening game for April 1. It is assume that if it
snows on April 1, 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 GHS 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 standard deviation of the amount that the insurance company
will have to pay.
A6. A hospital receives 20% of its COVID-

Answer 1

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

EY=0*0.5488+1000*0.3293+2000*0.1219=573.1

EY²=0²*0.5488+1000²*0.3293+2000²*0.1219=816900

VarY=EY²-(EY)²=816900-573.1²=488456

SD=$\sqrt{488456}$   =699