At a discount brokerage, a stock purchase or sale worth up to (and including) $7

Question

At a discount brokerage, a stock purchase or sale worth up to (and including) $7500 incurs a brokerage fee of 1% ofthe value ofthe transact on A transaction worth more than $7500 incurs a fee of $75 plus 0.5% of the amount exceeding $7500. Note that for a fraction of a cent, the brokerage always charges the customer a full penny. You wish to buy 100 shares of a stock whose price D in dollars has PMF PD(d) = 0 otherwise. (a) Find the PMF of C, the cost of buying the stock (including the brokerage fee). Pc(c) 0 otherwise. (b) Compute the expected value:

Explanation / Answer

(A) Here if d = $74.75

C = 74.75 * 100 * 1/100 = $ 74.75

if d = $75.00

C = 75.00 * 100 * 1/100 = $ 75

if d = $ 75.25

C = 75 + (0.25 * 100 * 0.5/100) = $ 75.125 or $ 75.13 (Penny must be rounded off)

PC(c) = 1/3 ; c = $ 74.75, $ 75.00 , $ 75.13

(b) E(C) = 1/3 * [74.75 + 75.00 + 75.13] = $ 74.96

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