x 0 1 2 3 4 5 f(x) 0.10 0.12 0.25 0.30 0.20 0.03 (i) What is the probability tha

Question

x 0 1 2 3 4 5

f(x) 0.10 0.12 0.25 0.30 0.20 0.03

(i) What is the probability that on any given day the convenience store sells exactly two copies of the journal.

(ii) In particular, the store needs to sell at least 3 copies per day to make a profit from the sale. What is the probability that the store will make profit on any given day?

(iii) Compute the expected value of the number of copies of the journal that will be sold daily.

(iv) Compute the standard deviation of the number of copies the journal that will be sold daily.

(v) Compute the cumulate distibution function of X.

Explanation / Answer

(i)

P(x=2) = 0.25

(ii)

P(x>=3) = 0.30 + 0.20 + 0.03 = 0.53

(iii)

E(x) = 0*0.1 + 1*0.12 + 2*0.25 + 3*0.30 + 4*0.20 + 5*0.03 = 2.47

(iv)

Var(x) = E(x2) - (E(x))2

E(x2) = 0*0.1 + 1*0.12 + 4*0.25 + 9*0.30 + 16*0.20 + 25*0.03 = 7.77

So, Var(x) = 7.77 - 2.472 = 1.67

Standard deviation of x = (Var(x))0.5 = 1.29

(v)

C.D.F of x:

x 0 1 2 3 4 5

cdf(x) 0.10 0.22 0.47 0.77 0.97 1.00

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