(a) Determine the distribution of the random variable C. Hint: Consider the possible child sequences in birth order, such as BBG (two boys and then a girl). Think how the sequences are generated, starting from the first child. Determine the probabilities of the sequences, and stop when appropriate. (b) Determine the joint distribution of G and B. (c) With what probability does the family have more girls than boys? (d) Determine the joint distribution of C and G.
(a) Determine the distribution of the random variable C. Hint: Consider the possible child sequences in birth order, such as BBG (two boys and then a girl). Think how the sequences are generated, starting from the first child. Determine the probabilities of the sequences, and stop when appropriate. (b) Determine the joint distribution of G and B. (c) With what probability does the family have more girls than boys? (d) Determine the joint distribution of C and G.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:(Family planning) A couple decides to have children until at least one of the following
conditions is fulfilled:
• They have two girls.
. They have four children in total.
Children are born one at a time, so that each child is a girl or a boy with equal probabilities,
independent of the previous children. Let us inspect the situation after the couple has stopped
having children (so at least one of the above conditions has been fulfilled). Let the total number
of children be C = G + B, where
G the number of girls,
B
the number of boys.
=
=
(a) Determine the distribution of the random variable C. Hint: Consider the possible child
sequences in birth order, such as BBG (two boys and then a girl). Think how the sequences are
generated, starting from the first child. Determine the probabilities of the sequences, and stop
when appropriate.
(b) Determine the joint distribution of G and B.
(c) With what probability does the family have more girls than boys?
(d) Determine the joint distribution of C and G.
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