interview questions shared by candidates
How much would you be willing to pay to join the following game? Start with 0 dollars on the table. You flip a fair-sided coin. If the coin is heads, I add another dollar, and you flip again. If the coin is tails, you walk away with the cash on the table.
Use binomial distribution to express the expected cash on the table after N rounds.... In series form, one can see that the summation does not converge...the expected cash is INFINITY.
there are 50% chances to win a dollar, 25% for 2 dollars, 12.5% for 3 and so on... there are also 50% chances to loose your investment! So the chance to win N dolars is .5^N this is aslo the chance to match your investment of N dollars. N % 0 100 1 50 2 25 3 12.5 4 6.25 5 3.125 ... Now is about what kind of risks you may want to take: 1 dollar - you are a moderate risker; 2 dollars - better; 3, 4 - high risk invester; 5, 6 - caution! 7 or more - stupid? Pesonaly I would preffer to go with 0 - you may not win but you cannot loose; but it wouldn-t work... (will it?) So I'll start with 1 and I'll negociate up to 2 or 3. (binomial distribution?!?)
As stated it seems my winnings = # of heads flipped before the first tails. This has a geometric distribution. So I would pay $1 or less to play (mean of the distribution), assuming a linear utility function.
You are the leader of a gang of n pirates who has just returned from a successful treasure hunt. You will make a suggestion about how to divide up the treasure and then a vote will be held. If you get a majority vote, your suggestion is accepted, the treasure is divided that way, and you all move on. If your suggestion is turned down, the other pirates kill you and the next one down the chain of command makes a suggestion and the cycle continues in that fashion until a method is decided upon. Your fellow pirates are reasonable and will know the best deal they can get if you suggest it. Your vote does count for your own offer but, in the event of a tie, you lose. Finally, assume that the gold supply to divide is infinite. What discrete offers are available at which ranges of values for n which get you the greatest amount of gold and allow you to keep your life?