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I am trying to figure out the probability, expected value, variance, and standard deviation for a...

I am trying to figure out the probability, expected value, variance, and standard deviation for a series of dice rolls. For example, if I roll a six-sided die in an attempt to roll a 1, and it takes me 13 rolls before a 1 appears, what are those answers? I believe I have figured out the probability equation:

P(P-1)^x where x is the number of rolls - 1 so for 13 rolls the probability would be: 1/6(1-1/6)^12 = .01864045

Is this the correct equation?

What equations would I need to find Expected Value, Variance, and Standard Deviation?

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