When the degrees of freedom in the chi-square distribution (see the previous exercise) is 1, the probability
Question:
When the degrees of freedom in the chi-square distribution (see the previous exercise) is 1, the probability density function is given by
Calculating probabilities is now complicated by the fact that the density function cannot be antidifferentiated. Numerical integration is complicated because the density function becomes unbounded as x approaches 0.
(a) Show that one application of integration by parts allows P(0 < X ≤ b) to be rewritten as
(b) Using Simpson’s rule with n = 12 in the result from part (a), approximate P(0 < X ≤ 1).
(c) Using Simpson’s rule with n = 12 in the result from part (a), approximate P(0 < X ≤ 10).
(d) What should be the limit as b → ∞ of the expression in part (a)? Do the results from parts (b) and (c) support this?
Step by Step Answer:
a Using integration by parts Thus b Notice that Using Simpsons rule with ...View the full answer
