Consider the population regression of log earnings [y, where y = ln(earnings)] against two binary variables: whether a worker is married (d_1, where d_1 = 1 if the person is married) and the worker's gender (d_2, where d_2 = 1 if the person is female), and the product of the two binary variables y = beta_0 + beta_1 d_1 + beta_2 d_2 + beta_3 (d_1 times d_2) + u. the interaction term (d_1 times d_2) allows the population effect on log earnings of being married to depend on gender does not make sense since it could be zero for married males indicates the effect of being married on log earnings cannot be estimated without the presence of a continuous variable

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560