"Would be fun if we were random variables."
Riku suddenly said. The usual abruptness.
"What do you mean?" Yuki asked back.
"I mean, values randomly determined, right? Different personalities every day."
Aoi laughed. "In a sense, all humans might be random variables. Because behavior isn't completely predictable."
"What's a random variable?" Yuki returned to basics.
"Mathematical representation of random phenomena. For example, dice rolls are random variables. Takes one of 1 to 6, but which is determined by probability."
Riku showed interest. "Then my tardiness is also a random variable?"
"Could say so. The random variable 'Riku's arrival time.' Expected value 9:10, variance about 10 minutes?"
"Expected value?"
"Average value of a random variable. E(X) = Σ x・P(x). Multiply each value by probability and sum."
Yuki calculated. "For dice, (1+2+3+4+5+6)/6 = 3.5"
"Correct. Dice expected value is 3.5. But 3.5 never actually comes up."
Riku tilted his head. "A value that doesn't appear is the expected value? Feels weird."
"Expected value is long-term average. With many trials, the average approaches 3.5."
Aoi continued. "And variance represents 'spread.' Var(X) = E[(X - E(X))²]. How much it deviates from expected value."
"High variance means unpredictable?" Yuki asked.
"Right. Low variance means always settling near expected value. High variance means sometimes deviating greatly."
Riku thought. "My arrival time has high variance. Sometimes I come at 8, sometimes 10."
"Well, something like that," Aoi smiled wryly.
Yuki wrote in the notebook. "Then Aoi-senpai's arrival time is low variance? Because always precise."
"Both expected value and variance small. High predictability random variable."
Riku clapped. "Then let's do a random variable conversation play, us three!"
"Conversation play?"
"I'm high-variance random variable-kun. Aoi-senpai is low-variance random variable-san. Yuki is... somewhere in between?"
Yuki laughed. "True, I'm not extreme."
Aoi went along. "Interesting. So, high-variance-kun, what's your next action?"
Riku said exaggeratedly. "Don't know! I'm high variance, so unpredictable!"
"But you have an expected value, right?" Yuki retorted.
"Um, expected value is 'act normally,' but since variance is large, sometimes I do outrageous things!"
Aoi continued. "I'm low variance, so I always act according to expected value. High stability."
"Isn't that boring?" Riku asked.
"Also means high reliability. In system design, low variance is often preferred."
Yuki joined. "I'm medium variance. Mostly predictable, but occasionally surprising."
"Good balance," Aoi acknowledged.
Riku suddenly became serious. "But you know, random variables are ultimately determined by probability distribution, right?"
"Sharp. Random variable properties are completely described by its probability distribution. Expected value and variance can be calculated from distribution."
"Then if I improve my 'tardiness distribution,' I'd be more trusted?"
"Statistically, yes. But moderate randomness might also be charm," Yuki laughed.
Aoi summarized. "Random variables are tools to handle uncertainty mathematically. Human behavior can be modeled as random variables to some extent."
"But if completely predictable, wouldn't be interesting, right?" Riku said.
"That's human goodness. Moderate uncertainty enriches relationships."
Yuki nodded. "We as random variables. Having expected value, having variance, having probability distribution."
"Because each has different distribution, conversation is interesting."
The three random variables were intersecting in the club room again today.