Let X be chi-squared with k = 5 degrees of freedom.
(a) What is P[X > 1]? (This exact calculation requires some serious integration)
(b) Find P[X > 1] with the normal approximation, i. e., approximate that probability assuming X ~ N(mu, sigma squared), where mu and sigma squared are the mean and variance of a Gamma(5/2, 1/2).
a)
using R
P(X > 1) = 0.9625658
pchisq(x,df) gives P(X < x) where X follow chi-square with degree of freedom = df
1-pchisq(1,5) [1] 0.9625658
2)
mean = df = k = 5
variance = 2*df = 2*k = 10
P(X > 1)
= 0.8970484
1-pnorm(1,5,sqrt(10)) [1] 0.8970484
Let X be chi-squared with k = 5 degrees of freedom. (a) What is P[X >...
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