"Can people be represented by probability distributions?"
Yuki murmured absently. The three were studying in a corner of the library.
"What do you mean?" Riku looked up.
"A person's behavior patterns. Can they be predicted probabilistically?"
Aoi showed interest. "An interesting question."
"For example," Yuki continued. "The probability of Riku being late."
"Me?" Riku was surprised.
"Monday, 30 percent. Friday, 10 percent."
"Why is Friday lower?"
"Because the weekend is near, you're in a better mood?" Yuki laughed.
Aoi opened their notebook. "Representing people through probability distributions is meaningful from an information theory perspective."
"Meaningful?"
"You can calculate expected value. E(X) = Σ x・p(x)"
Riku tilted his head. "What's expected value useful for?"
"You can predict average behavior. For example, how many times Riku will be late in a week."
"About 1.5 times?" Yuki guessed.
"That's expected value. Actually it's 1 or 2 times, but on average it's 1.5."
Riku protested. "But I'm unpredictable."
"That's variance," Aoi explained. "Deviation from expected value. Var(X) = E[(X-μ)²]"
"The larger the variance, the harder to predict."
"Riku has high variance," Yuki understood.
"That's not a compliment, is it?"
Aoi smiled. "It's a neutral observation."
"What about Aoi-senpai?" Yuki asked.
"I might be low variance. Because I'm regular."
"But isn't that boring?" Riku said.
"Not necessarily. Predictability leads to trust."
Yuki thought. "Trust and predictability are related."
"Yes. When you can predict someone's behavior, you feel secure. Low variance means high reliability."
Riku joked. "So I'm not trusted?"
"No," Yuki hurried to say. "Riku has high expected value. You're occasionally late, but your kindness has high expected value."
"Expected value of kindness?"
"Yes. High probability of helping people in trouble. That's Riku's characteristic."
Aoi nodded. "People have multiple probability distributions. Distribution of lateness, distribution of kindness, distribution of concentration."
"It's complex," Riku groaned.
"That's why it's interesting. Can't be measured by simple expected value alone."
Yuki wrote in her notebook. "Looking at people through probability distributions lets you understand them multidimensionally."
"Right. And variance matters too. Variation is individuality."
Riku said happily, "So my high variance is individuality?"
"Well, yes," Aoi admitted.
"But," Yuki said seriously. "I want you to be low variance when it matters."
"When it matters?"
"Promises. Exams. I want you to be predictable at those times."
Riku was embarrassed. "Got it. I'll adjust variance by situation."
Aoi laughed. "Adaptive probability distribution."
"People aren't fixed. They change with situations."
Yuki looked out the window. "Maybe friendship is learning each other's probability distributions."
"Good insight," Aoi was impressed.
"Knowing each other's expected values and variances. And accepting them."
Riku continued. "Even if you can't predict perfectly, it's enough to mostly understand."
"Exactly. Enjoying uncertainty is also friendship."
Aoi said quietly. "Information theory tends to see uncertainty as an enemy, but in human relationships it's different."
"Different?"
"Moderate uncertainty enriches relationships. If perfectly predictable, it's boring."
Yuki laughed. "So Riku's high variance has meaning."
"That's right."
The three looked at each other. Different probability distributions each. But there are overlapping parts.
"What kind of probability distribution is our friendship?" Riku asked.
"High expected value and moderate variance," Aoi answered.
"Perfect," Yuki smiled.
Beyond probability, there's a certain bond. Something that can't be expressed in formulas connected the three.