Show the student_t(20, 0, 2) in brms prior in R

 Here is to show the prior student_t(20, 0, 2) from brms in R:

# Parameters

df <- 20     # degrees of freedom

mu <- 0      # mean (location)

sigma <- 2   # scale


# Define x range (say, ±4 standard deviations)

x <- seq(mu - 5*sigma, mu + 5*sigma, length.out = 1000)


# Student-t density

y <- dt((x - mu) / sigma, df = df) / sigma


# Plot

plot(x, y, type = "l", lwd = 2, col = "blue",

     main = "Student-t(20, 0, 2)",

     xlab = "x", ylab = "Density")

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