"We're like random variables, aren't we?"
Riku said out of nowhere.
"Huh?" Yuki was surprised.
Aoi asked with interest. "What do you mean?"
"Well, we're always unpredictable. Me, Yuki, Aoi-senpai."
"Interesting perspective," Aoi smiled. "Actually, human behavior can be modeled probabilistically."
"What do you mean?" Yuki asked.
"Random variable X is a variable that takes values probabilistically," Aoi explained. "For example, Riku's tardiness time tomorrow, X."
"That's a harsh example," Riku laughed.
"But appropriate. From 0 to 30 minutes, with a probability distribution."
Mira quietly wrote in her notebook. "X ~ Distribution"
"Probability distribution," Aoi explained. "What values, with what probabilities."
Yuki began to understand. "Each person has a different distribution?"
"Yes. Riku's tardiness time might be close to uniform distribution."
"Meaning random?"
"Equally late," Aoi laughed.
Riku countered. "Yuki is normal distribution. Always about the same time."
"Normal distribution?"
"Distribution concentrated around the mean value," Aoi explained. "Meaning stable."
Yuki was a bit embarrassed. "Is that a compliment?"
"It is," Riku said.
Mira showed a note. "E[X] = mean, Var[X] = spread"
"Expected value and variance," Aoi translated. "Expected value is average value, variance is spread."
"My variance seems high," Riku self-acknowledged.
"Indeed. Hard to predict."
Yuki asked. "What's your distribution, senpai?"
Aoi thought. "I might be... binomial distribution."
"Binomial distribution?"
"Success or failure. Whether explanations go well or not."
"Senpai, you always do well," Riku said.
"There are failures you don't see."
Mira wrote a new note. "Independence: P(X,Y) = P(X)P(Y)"
"Independence," Aoi explained. "When two random variables don't affect each other."
"Are we independent?" Riku asked.
"Not completely independent," Aoi answered. "There's correlation."
"Correlation?"
"One's value affects the other."
Yuki gave an example. "When Riku is late, the meeting is delayed."
"That's correlation," Aoi acknowledged.
Riku laughed. "I'm having a bad influence."
"But there's good correlation too."
"Like what?"
"Riku's jokes and good atmosphere," Aoi said. "Positive correlation."
"Oh, I got praised."
Mira smiled and wrote. "Cov(X,Y) = E[XY] - E[X]E[Y]"
"Covariance," Aoi explained. "Measures correlation strength."
Yuki thought. "How correlated are we?"
"Pretty high I think," Aoi answered. "Because we spend a lot of time together."
"But if completely correlated?" Riku asked.
"One determines the other. That's boring."
"Too independent means no relationship," Yuki added.
"Moderate correlation is good," Aoi nodded. "Influence each other but maintain uniqueness."
Riku looked outside. "After school with random variables."
"Good title," Yuki laughed.
Mira wrote a summary. "Different distributions, positive correlation, unique variance"
"Different distributions, positive correlation, unique variance," Aoi translated.
"That's us," Riku said.
The four nodded. Unpredictable like random variables. But with probability distributions. And certainly connected. That's the reality of after school.