---
title: "R Laboratuvarı 9: Ortak dağılımlar"
format: html
execute:
  echo: true
  warning: false
---

İki sensör ortalamasının belirsizliği üç korelasyon senaryosunda karşılaştırılır.

~~~{r}
shift_probability <- c(0.5, 0.5)
shift_mean_MPa <- c(100, 106)
shift_variance_MPa2 <- c(4, 4)
overall_mean_MPa <- sum(shift_probability * shift_mean_MPa)
within_MPa2 <- sum(shift_probability * shift_variance_MPa2)
between_MPa2 <- sum(shift_probability * (shift_mean_MPa - overall_mean_MPa)^2)
stopifnot(all.equal(within_MPa2 + between_MPa2, 13))

knitr::kable(
  data.frame(
    olcu = c("genel ortalama", "vardiya içi varyans", "vardiyalar arası varyans", "toplam varyans"),
    deger = c(overall_mean_MPa, within_MPa2, between_MPa2, within_MPa2 + between_MPa2),
    birim = c("MPa", "MPa^2", "MPa^2", "MPa^2")
  ),
  digits = 2,
  caption = "Toplam varyans ayrışımı"
)
~~~

```{r}
sd_x <- 0.8
sd_y <- 1.2
rho <- c(0, 0.5, -0.5)
cov_xy <- rho * sd_x * sd_y
var_mean <- 0.25 * sd_x^2 + 0.25 * sd_y^2 + 0.5 * cov_xy
sonuc <- data.frame(
  korelasyon = rho,
  kovaryans_C2 = cov_xy,
  ortalama_hatasi_ss_C = sqrt(var_mean)
)
knitr::kable(sonuc, digits = 3, caption = "Korelasyon ve birleşik sensör belirsizliği")
```