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A certain small town, whose population consists of 100 families, has 30 families with 1
Chapter 4, Problem 7(choose chapter or problem)
A certain small town, whose population consists of 100 families, has 30 families with 1 child, 50 families with 2 children, and 20 families with 3 children. The birth rank of one of these children is 1 if the child is the firstborn, 2 if the child is the secondborn, and 3 if the child is the thirdborn. (a) A random family is chosen (with equal probabilities), and then a random child within that family is chosen (with equal probabilities). Find the PMF, mean, and variance of the childs birth rank. (b) A random child is chosen in the town (with equal probabilities). Find the PMF, mean, and variance of the childs birth rank.
Questions & Answers
QUESTION:
A certain small town, whose population consists of 100 families, has 30 families with 1 child, 50 families with 2 children, and 20 families with 3 children. The birth rank of one of these children is 1 if the child is the firstborn, 2 if the child is the secondborn, and 3 if the child is the thirdborn. (a) A random family is chosen (with equal probabilities), and then a random child within that family is chosen (with equal probabilities). Find the PMF, mean, and variance of the childs birth rank. (b) A random child is chosen in the town (with equal probabilities). Find the PMF, mean, and variance of the childs birth rank.
ANSWER:Step 1 of 4
(a)
Define following random variable
Observe that . Let's find PMF. Using LOTP we have