Probability mass function for Exercise 5.8, age of mother atbirth of child. Age

Question

Probability mass function for Exercise 5.8, age of mother atbirth of child. Age                        10-14      15-19      20-29   30-39      40-44      45-49 Age midpoint         12.5         17.5         25         35            42.5         47.5 Pr(X=x)                  0.003      0.100      0.500    0.300      0.097         0.000 a.) If we select a birth at random, what is the probabilitythe mother is 19 years of age or younger? b.) What is the probability she is 30 years of age orolder? c.) What is the expected age of the mother at birth? (Use agemid-points for your calculations.) d). What is the variance of mothers'ages?         Probability mass function for Exercise 5.8, age of mother atbirth of child. Age                        10-14      15-19      20-29   30-39      40-44      45-49 Age midpoint         12.5         17.5         25         35            42.5         47.5 Pr(X=x)                  0.003      0.100      0.500    0.300      0.097         0.000 a.) If we select a birth at random, what is the probabilitythe mother is 19 years of age or younger? b.) What is the probability she is 30 years of age orolder? c.) What is the expected age of the mother at birth? (Use agemid-points for your calculations.) d). What is the variance of mothers'ages?        

Explanation / Answer

(a) P(X=30)=0.300+ 0.097 +0.000 =0.397 (c) E(X)= 12.5* 0.003 +17.5* 0.1 +25* 0.5 +35* 0.3 +42.5*0.097 +47.5*0= 28.91 (d) E(X^2)=12.5^2* 0.003 +17.5^2* 0.1 +25^2* 0.5 +35^2* 0.3+42.5^2* 0.097 +47.5^2*0=886.3 Var(X)= E(X^2) - [E(X)]^2            =886.3 - 28.91^2            =50.5119

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