Every-day-for-n-days-you-put-either-1-2-or-3-into-a-saving-account-It-is-random-as-to-how-much-you-save-each-day-What-is-the-average-amount-you-will-have-saved-in-n-days-

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Question Number 8232 by FilupSmith last updated on 03/Oct/16

$$\mathrm{Every}\mathrm{day},\mathrm{for}n\mathrm{days},\mathrm{you}\mathrm{put}\mathrm{either}$$$$\mathrm{\$}1,\mathrm{\$}2,\mathrm{or}\mathrm{\$}3\mathrm{into}\mathrm{a}\mathrm{saving}\mathrm{account}.$$$$\mathrm{It}\mathrm{is}\mathrm{random}\mathrm{as}\mathrm{to}\mathrm{how}\mathrm{much}\mathrm{you}\mathrm{save}$$$$\mathrm{each}\mathrm{day}.\mathrm{What}\mathrm{is}\mathrm{the}average\mathrm{amount}$$$$\mathrm{you}\mathrm{will}\mathrm{have}\mathrm{saved}\mathrm{in}n\mathrm{days}?$$

Answered by prakash jain last updated on 03/Oct/16

$$\mathrm{Assuming}\mathrm{uniform}\mathrm{distribution}.$$$$\mathrm{On}\mathrm{an}\mathrm{average}\mathrm{you}\mathrm{will}\mathrm{save}=\frac{1+2+3}{3}=\mathrm{\$}2$$$$\mathrm{every}\mathrm{day}.$$$$\mathrm{So}\mathrm{you}\mathrm{will}\mathrm{save}2n\mathrm{dollars}\mathrm{after}\mathrm{n}\mathrm{days}.$$

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