Question below is pmf of Z:

 Z P(Z) -3 1/16 -2 1/8 -1 3/16 0 1/4 1 3/16 2 1/8 3 1/16

a)E(Z) =ΣzP(z) = 0

b) P(Z=-1 |Z<1) =P(Z=-1)/P(Z<1) =(3/16)/(5/8)=3/10 =0.3

c) P(Z=2 in fourth attempt) =P(first 3 failures and 4th failure) =(1-1/8)^3*(1/8)=343/4096

d) from binomial distribution: P(4 times out of 10) =C(10,4)*(1/4)4*(3/4)6 =0.1460

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