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

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Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented by random variable X and those of th

math Statistics-And-Probability

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Answer 1

Answer #1

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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Answer 2

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