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回复 #391 qian.qian 的帖子
P(d)=0.52
(a) What is the distribution of X? the probability distribution of the number Y = X − 1 of failures before the first success, should be Geometric distribution
(b) What is the probability that the couple will have at least 5 children?
cdf for Geometric distribution = 1-(1-p)^k
Note P(at least 5)=1-P(k<=4)
therefore P(K>=5)=1-P(K<=4)=1-[1-(1-p)^k]=(1-p)^k=...
(c) Find E[X].
E(X)=1/p
(d) A different childless couple (with the same birth probabilities) decide to keep having children
until they have both a son and a daughter. Let Y be the number of children that they will have. Give an expression for P(Y = n) (hint: it is very helpful here to first condition on the
gender of the first child!)
to first condition on the gender:
-if first is a boy, E(X)=1/p
-if first is a girl, E(X')=1/q
the probability for get a boy is q and for girl is p therefore E(Y)=qE(X)+pE(X')
z-score, would you check if I'm right? haven't been playing with this for a long time. |
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