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**undefined** I don't know what you mean, but in fact P(X=2) = 1/4. This is because in order to end at 2 throws, we must throw odd then even, so (1/2)(1/2) = 1/4. Similarly, to end at three throws we must throw odd then odd then even, and P(X=3) = 1/8.

We get the sum E(X) = 1/2 + 2/4 + 3/8 + 4/16 + 5/32 + ...

Above I mention a method of evaluating the sum, after which we will get E(X) = 2. Like I wrote above, the way I found seems kind of messy, but maybe that's a standard way, don't really know. If you want me to show you I can.