Variance for mixed distribution (continuous + discrete)

probability statistics

Solution 1:

The CDF as given explicitly states that Pr{ X < 1 } = 0, so the answer to your first question is NO, it is not ½.

However, the CDF jumps from 0 to ½ at X = 1. Therefore we know that Pr{ X = 1 } = ½.

I think this will be enough to get you started on the answer. I could work it all out for you, but it looks like a homework problem so I think I will stop here.

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