Probability and Regression Analysis

Probability and Regression Analysis
Part 1
Question 1
(a). Probability (have a second child) = 0.684
(b). Probability (have a second | 1st child a boy) = 0.326
(c). Probability (have a second | 1st child a girl) = 0.358
(d). Yes, the events “have a second child) and “sex of first child” are independent events simply because one
event does not affect the outcome of the other. Regardless of whether the couple had a boy or girl the first time
the decision to have a second child is entirely influenced by the parents.
Question 2
(a). No, the two variables X and Y are not independent simply because X can be computed using a function of
Y
(b). No, the two variables X and Y are correlated i.e.
The expected value of the product of two independent variables is the product of expected value of those two
variables. That’s not the case here.
E ( X . Y ) =E ( X ) . E(Y )
E ( X . Y ) =E ( Y 2 ) . E(Y )
E ( X . Y )=E ( Y 3 )
E ( X . Y )=E ( Y 3 ) =0
In addition their covariance is also 0 i.e. cov(X,Y)=0
(c). Uncorrelated variables are independent. FALSE
(d). Independent variables are uncorrelated. TRUE
Question 3
The slopes are not reciprocals
With regard to basic statistical representation of the aforementioned problem we can see that
Y =ax+b where a isthe slope