I am trying to figure out the probability, expected value,variance, and standard deviation for a series of dice rolls. Forexample, if I roll a six-sided die in an attempt to roll a 1, andit takes me 7 rolls before a 1 appears, what are those answers? Ihave figured out the probability equation:
P(P-1)^x where x is the number of rolls - 1 so for 7 rolls theprobability would be: 1/6(1-1/6)^6 = 0.05581632...
Further where I am lost is taking the above and using it to findthe Expected Value, Variance, and Standard Deviation?
As I see the equations but plugging in numbers has me lost as pis the probability of failure and x = 0,1,2,3 for geometricdistribution it would be
E(X)= (1-p)/p .... this is where I am lost as failure is 5/6 not1/6 correct? Please show example of this so I can betterunderstand, also on Variance, and Standard Deviation?
