Nora Bakery would like to determine how many birthday cakes to bake at the beginning of each day in order to lnaxil'nize the daily expected prot. Each birthday cake costs the bakery $10 and it can be sold for $35 each. However, all leftover birthday cakes at the end of each day will be donated to nonprot organizations. Due to the manpower restriction, the bakery can only bake no more than ve cakes in one day. Statistical analysis has shown that the daily demand of cakes is a randon'l variable with the following probability mass function: Let X be net prot per day if ve birthday cakes are baked in each day. a Find the probability mass function of X. Find the mean and standard deviation of X. ( J (b) Find the clnnnlative distribution function of X. ((1 ( l d Will the expected profit be higher if only [our birthday cakes are baked in each day? Justify your