Annual profit ( P ) is the product of total annual sales ( S ) and profit per un

Question

Annual profit

(P)

is the product of total annual sales

(S)

and profit per unit sold

(X);

that is,

Pequals=Xtimes•S.

It is desired to know the probability distribution of the random variable P when X and S have the following assumed probability mass functions

(X

and S are independent). What are the mean, variance, and standard deviation of the probability distribution for annual profit,

P?

Annual proft (P) is the preduct of tetal amual sales (S)and profit per unit soid tha is PX.I is desired to know the probabiity dstiburon of the random variable Pwhen Xand 3 havethe clowing aseurmed crebabilty maes tunctions (X and S are independent Vha ae the mean van co, and standard devation of te probability astroubon for anrual profit p> X (Unit Profit) alue Probabll S(Annual Sales Value Probabllty 04 0.1 0.5 0.25 The mean isRaud to twa derimal paes ) lhe vanarice is (Round to three decimal places. The sla·luaid deviain is l I. tRuund lu INC decimal places.)

Explanation / Answer

excel formulation

X p S p 0 0.05 5 0.4 1 0.45 8 0.1 2 0.25 9 0.5 3 0.25 P p P*p P^2*p 0 0.05 0 0 5 0.18 0.9 4.5 8 0.045 0.36 2.88 9 0.225 2.025 18.225 10 0.1 1 10 16 0.025 0.4 6.4 18 0.125 2.25 40.5 15 0.1 1.5 22.5 24 0.025 0.6 14.4 27 0.125 3.375 91.125 1 12.41 210.53 mean 12.41 variance = 56.5219 sd 7.518105

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