Burst PMF

pmfx  =  
        Function[{x, p},  (((1 - p))^(x - 1)) p ]

Plot[pmfx[x,  .2], {x, 1, 10}]

Burst CDF

cdfy  =   Function[{y, 
            p}, (∑_(x = 1)^y)(((1 - p))^(x - 1)) p ]

Plot[cdfy[y,  .2],  {y, 1, 10}]

Burst Mean

m=(∑_(x = 1)^∞)(((1 - p))^(x - 1)) 
            p x

m=Simplify[m]

Burst Variance

v=(∑_(x = 1)^∞)(((1 - p))^(x - 1)) 
            p (((x - m))^2)

v = Simplify[v]

Burst Standard Deviation

s =Simplify[(Sqrt[v])]