# CS 70 Reading Quiz -- Week 13, Sunday

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1. Suppose that 90% of web merchants that sell light bulbs are sleazy: they'll sell you a light bulb that has a 1/20 chance of burning out on any day. The remainder 10% of web merchants use high-quality merchandise: their bulbs have a 1/1000 chance of burning out on any given day. Sadly, you can't distinguish the two types of merchants apart from their web site -- they all look identical.

I pick a web merchant at random, buy a dozen bulbs from them, and install the first bulb in my kitchen. Let the random variable X denote the number of days until it burns out. When it burns out, I curse loudly, then replace it with another bulb from the same merchant (because I've got to use them up). Let the random variable Y denote the number of days until the second bulb burns out (counting from the day when we replaced the first bulb).

Question: Are the random variables X and Y independent?

2. Let X,Y be as above. Let the random variable Z denote the total number of days until the second bulb burns out, so that Z = X+Y.

Question: Are we guaranteed that E[Z] = E[X] + E[Y]?

3. Let X,Y,Z be as above. Question: Are we guaranteed that Var(Z) = Var(X) + Var(Y)?

4. What did you find difficult or confusing about the reading or the lectures, and what would you most like to see explained better? If nothing was difficult or confusing, and you understand the material pretty well, tell us what you found most interesting. Please be as specific as possible.