The textbook formula for the variance of the discrete random variable Y is given as 
Another commonly used formulation is 
.
Prove that the two formulas are the same.
Definitions:
Just-world Hypothesis
The cognitive bias that assumes that actions always yield morally fair and fitting consequences, essentially that the world is just.
Groupthink
A psychological phenomenon that occurs within a group of people when the desire for harmony or conformity in the group results in an irrational or dysfunctional decision-making outcome.
Symptoms
Signs or indications of a disease, disorder, or condition, often experienced by the individual affected.
Solomon Asch
A psychologist known for his research on conformity, including his famous experiment demonstrating how group pressure can influence an individual to conform.
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