1. Suppose on any.r given day, the probability that you stub your toe is .04. The probability that your clumsy friend stubs their toe is .12. Assume days are independent. {3.) Give the binomial distribution for X, the number of times you stub your toe in 190 days, and for Y, the number of times your friend stubs their toe in 1(1) days. (b) What is the Poisson distribution that you can use to npprmciinate Z = X + Y? (e) Using the Poisson distribution from part (b), nd P(Z : 20). {(1) Find V00 + V(Y) using the binomial distributions from part {11]. Next, nd V(Z] using the Poisson distribution from part (b). Which expmion for variance is larger? Give an intuitive explanation for why this is the ease