This is the pmf table for age of mothers at birth of child inthe US Age 10-14 15

Question

This is the pmf table for age of mothers at birth of child inthe US Age                      10-14      15-19      20-29      30-39      40-44      45-49 Age mid-point      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* *Less than .0005 Questions: a. If we select a birth at random, what is the probability themother 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 agemidpoints for your calculations.) d. What is the variance of mothers ages?          MYQUESTIONS- 1. What is x? 2. Please explain how to get the answer to a and b? 3. Answer C - I calculated the expected age to be 76.4 and Iknow this is incorrect. The formula I used was age xPr(X=x). Please explain 4. If C's answer is wrong D will also be wrong. Pleaseexplain D. This is the pmf table for age of mothers at birth of child inthe US Age                      10-14      15-19      20-29      30-39      40-44      45-49 Age mid-point      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* *Less than .0005 Questions: a. If we select a birth at random, what is the probability themother 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 agemidpoints for your calculations.) d. What is the variance of mothers ages?          MYQUESTIONS- 1. What is x? 2. Please explain how to get the answer to a and b? 3. Answer C - I calculated the expected age to be 76.4 and Iknow this is incorrect. The formula I used was age xPr(X=x). Please explain 4. If C's answer is wrong D will also be wrong. Pleaseexplain D.

Explanation / Answer

Let x be the age. (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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