Here’s an example: Byrne et al. (2018) ran an experiment in the…

Here’s an example:
Byrne et al. (2018) ran an experiment in the state of Victoria in Australia to
see how electricity consumption of households vary with information on energy use.
In the experiment, some households frequently received accurate information about
their energy use, as well as that of their neighbors. Other households received no
such information. They found that households that overestimate or underestimate
their electricity consumption end up consuming more electricity when receiving the
information on energy consumption.”

In this paper, the population Ω is the collection of households in Victoria, Aus-
tralia. ω is a single household. X is the receipt of information on electricity con-
sumption, and Y is electricity consumption.

1. Angrist and Evans (1998) investigate how the number of children in a household
impact whether the mother works (i.e., is employed), as well as the number of
hours worked each week. The study focuses on households in the US with two
or more children. The estimates in the paper suggest that having a third child
causes a 20% reduction in women’s labor supply (base rate of 57%). For the
women who work, there is a 25% reduction in the hours they work each week
(base rate of 18.8 hours per week).

(i) The sample space or “population,” Ω;
(ii) An outcome ω ∈Ω;
(iii) The random variable whose effect we are interested in, X;
(iv) The random variable that is affected, Y .

2. Baird et al. (2016) conducted an experiment in Kenya to estimate the long-
run impacts of child health investment. The authors introduced a deworming
program across schools as the health investment. Ten years later, the authors
found that the children who received the deworming treatment enroll for more
years of primary school, work 17% more hours each week, and experience a 2.8
percentage point decrease in miscarriage rates (relative to a 3.9% base rate)
compared to the children who did not receive the treatment.

(i) The sample space or “population,” Ω;
(ii) An outcome ω ∈Ω;
(iii) The random variable whose effect we are interested in, X;
(iv) The random variable that is affected, Y .

3. How much do parents value school quality? Black (1999) came up with the
clever idea of measuring school quality using housing prices. In Massachusetts,
students can only enroll in the local schools if they live in the corresponding
zone. So the authors looked at how house prices vary across school districts
in Massachusetts. They found that a 5% increase in elementary school test
scores leads to a 2.1% increase in the marginal resident’s willingness to pay for
housing.

(i) The sample space or “population,” Ω;
(ii) An outcome ω ∈Ω;
(iii) The random variable whose effect we are interested in, X;
(iv) The random variable that is affected, Y .
just follow the example