3. [5 marks] Say we have m balls numbered from 1 to m, and we have n bins numbered from 1 to n. We are throwing these balls one by one into the bins. When we throw a ball, it goes with equal probability of 1 into any of the n bins. What is the expected number of balls in bin number 1 after throwing all m balls into the bins? Hint: This problem is very easy if we define the random variables as follows. Assume that random variable Y represents answer which is the number of balls in bin 1. Also, assume that for each ball i we have a random variable X X is 1 if the b i goes to bin 1 and is 0 otherwise. So, we can say that Y + X2 + + Xm, because basically for each ball that goes into bin 1 we are adding 1 to the value of Y Now, compute EX for eac h i, and then compute ETY using linearity of expectation