Count trials through the first success

Here X counts the trial on which the first success occurs in independent trials with constant success probability p. The support is 1,2,3,... and p(x)=(1-p) raised to the power of x-1 ^x-1p. The first x-1 trials must fail and trial x must succeed. Another convention counts failures before success and starts at 0; always state which random variable is being used.