easy Probability
A release-checked easy problem for training Linearity of Expectation, Expected Value/LOTUS.
You are looking to drive to a friend's house. With no interruptions, this takes $m$ minutes to do. However, there are $n$ stoplights along the way labelled $1-n$. Stoplight $i$ stops you with probability $p_i$. Given that you are stopped by stoplight $i$, you are stopped for $L_i$ minutes. Find the expected amount of time it takes for you to reach your friends house when $m = 10, n = 4, p_i = 1/i,$ and $L_i = i$.
This Probability problem is tagged Linearity of Expectation, Expected Value/LOTUS. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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