At the one top pizza shop, mushrooms are the only topping. curiously, a pizza sold before noon has mushrooms with probability p = 1/3 while a pizza sold after noon never has mushrooms. also, a pizza is equally likely to be sold before noon as after noon. on a day in which 100 pizzas are sold. let n equal the number of pizzas sold before noon and let m equal the number of mushroom pizzas sold during the day.

a)what is the conditional pmf of m given n? are m and n independent?

b)what is the joint pmf of m and a/?

For example, the upper right cell shows that if expresso advertises and beantown doesn't advertise, expresso will make a profit of $15 million, and beantown will make a profit of $2 million. assume this is a simultaneous game and that expresso and beantown are both profit-maximizing firms. if expresso decides to advertise, it will earn a profit of $ million if beantown advertises and a profit of $ million if beantown does not advertise. if expresso decides not to advertise, it will earn a profit of $ million if beantown advertises and a profit of $ million if beantown does not advertise. if beantown advertises, expresso makes a higher profit if it chooses . if beantown doesn't advertise, expresso makes a higher profit if it chooses . suppose that both firms start off not advertising. if the firms act independently, what strategies will they end up choosing? expresso will choose to advertise and beantown will choose not to advertise. expresso will choose not to advertise and beantown will choose to advertise. both firms will choose to advertise. both firms will choose not to advertise.