使用R的概率样本估计

Question

Suppose I have a random sample of 100 observations from a population with distribution Y=X^2, where X is normal. How do I calculate the sample estimate of P(Y<=2) using R? Here P() denotes probability. Does the following code help?

X=rnorm(100)
Y=X^2
prob(Y<=2)

Thanks beforehand

Answer 1

If y = x^2 , then P(y <= 2) = P(x^2 <= 2) = P(x <= sqrt(2))

So, the answer is:

pnorm(sqrt(2)) - pnorm(-sqrt(2))
# [1] 0.8427008

Answer 2

Thanks to @markdly the required code is sum(Y<=2)/length(Y)

This calculates the probability that the sample observations are less than or equal to 2, which varies with sample. The above answer given by @akond, which basically calculates the exact probability could also be derived from pchisq(2,1)