bivariate_normal_distribution.scala

//https://www.ai-class.com/course/video/quizquestion/116
//Calculate the average and the covariance matrix.

val ls = List(3 -> 8, 4 -> 7, 5 -> 5, 6 -> 3, 7 -> 2)
val l = ls.map{case (a, b) => (a.toDouble, b.toDouble)}

def square(n:Double) = n*n
def mu(l:List[Double]):Double = l.sum/l.length
def sigmaSq(l:List[Double], mu:Double):Double = l.map(x=>square(x-mu)).sum/l.length

val mx = mu(l.map(r=>r._1))
val my = mu(l.map(r=>r._2))

val m = (mx, my)

val M = l.length
def sum2(t:(Double, Double)):Double = t._1 + t._2
val sigma = l.map{case (ax, ay) =>
    val dx = ax - mx
    val dy = ay - my
    List(dx*dx, dy*dx,dx*dy,dy*dy)
}.reduce{(a, b)=>a zip b map sum2}.map(_/M)

println("mu = "+m)
println("Sigma = "+sigma)