Jay has $500 in the bank when he decides to try a savings experiment. On each day i ∈ [1..30], Jay flips a fair coin. If it comes up heads, he deposits i dollars into the bank; if it comes up tails, he withdraws $10. How many dollars should he expect to have in the bank after 30 days?

$582.5

Step-by-step explanation:

Already has $500 in the account and there outcomes of the coin are equally likely to occur if it comes tails he withdraws   $10 so the expected change in a day is 1/2 (X-10)  X being number of the day we have to get a sum of these and add the opening amount of $500

1/2 ×sum of outcomes = 1-10 + 2-10+3-10 all the way to 30-10

= 165×1/2 =82.5

then total = 500+82.5=$582.5