给你个例子你就明白了：



n <- 100
y <- rnorm(n, 5, 1)

width <- 0.01
scal <- seq(-2, 12, by = 0.01)

ll <- length(scal)

den_y <- density(y, n = ll, from = -2, to = 12)  # here defines the range and width

plot(scal, den_y$y, type = "l")

# use numerical integration
# for example, you need pr(a < x < b)
a <- 2
b <- 4

begin <- which.max(den_y$x[den_y$x < a])
end <- which.max(den_y$x[den_y$x < b])


prob <- sum(den_y$y[begin:end]*width)

# confirm

true_prob <- pnorm(4, 5, 1) - pnorm(2, 5, 1)  # increase n to 100000, true_prob = prob. In small sample, they are different

谢谢楼上回答，对我很有启发，谢谢。

记得加分啊！

不太明白是什么意思，可以解释一下为什么这么求么？