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
Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented...
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