So we have ht+2h2t+3 h3t+ I’ll write next term 4h4t and this sum continues forever.
Well the first term is just zero so let’s just get rid of it. But how are you going to evaluate this sum. So we’ve reduced this relatively complicated problem to just as infinite sum. H3t and this is sum to infinity so this continues forever. If I introduce one more term, we have 3 times That’s to throw two heads and then a tail. So then we get h times t then what’s the probability of getting 2. You have to throw a one head and a tail right after that. The second term we are gonna get 1 times the probability of getting 1 well there’s only one way of getting 1. The probability of that happening is just t. Well there’s only way to get a £0 in the game total. So what’s the probability of you getting 0. Now I have to actually start finding these probabilities.
#Ifactor interview questions plus
1 times the probability of me getting 1 plus 2 times the probability of me getting 2 and you continue this on so it’s an infinite sum to infinity. It’s just 0 times the probability of me getting 0. If you are a bit confused by the summation notation with the sigma, I’ve also written it out like this. So in this case, the amount of money, I’m summing the amounts of money from let’s say i equals 0 to infinity. So you can get £1, you can get £2, £3, £4. So in this case, the outcomes will just be the amount of money you get and these will be integers. So the expectation is defined to be the amount of money you can get in some case, times the probability of getting that amount of that money and you sum for each possible outcome. I have to recall the definition of expectation. I’ll let H be the probability that you throw heads and I’ll let T be the probability that you throw tails. I will start by introducing some variables. The interview question is essentially what is the expectation, what is the average amount of money that you are going to get from this game. If you throw a head, you get one £1 and you get to continue so you throw again, if you throw a tail, you get nothing and the game ends. By that what I mean is the probability of throwing a head and a tail is not both a half. You play a game with a coin and the coin is not necessarily fair.
I study Maths at Oxford and today I’ll run through a very quick Maths interview question.
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