Given $k$ balls and $n$ buckets where $k\geq n$. Each ball is thrown, and with probability $p$ it lands in one of $n$ buckets. Each bucket is equally likely.
Let $X_i$ be a random variable represent number of ball in bucket $i$ What is the $E[X_i]?$
I assumed that success means the ball is actually in the bucket. I've tried finding $E[X_i]$ through $E[X] = E[X_1 + X_2 + ... + X_n]$. I feel like I'm going in wrong direction.
I've also tried $E[X] = kp$, so $E[X_i] = (kp)/n$