Iii Answer The Following Questions 1 2 Find The Value Of The Following Integral Exp 7 Dxcdy 2 8 8 1 N 1 (70.59 KiB) Viewed 21 times
III. Answer the following questions. 1. 2. Find the value of the following integral: = [ ] exp(-+*+7²) dxcdy 2 -8-8 1₁ Note that you may substitute x = r cos 0, y = r sin 0 (0 ≤ r < ∞,0 ≤ 0 < 2π) with real variables r and 0. (3) Find the value of the following integral by using the solution of Question III.1: ∞ 1₂ = [ exp(-ax²) dx ∞ Note that a is a positive constant. (4)
IV. Consider a test whether a person is infected with a virus or not. Assume that a rate x of people infected with the virus in the community is x = 0.001 and a prior probability that a person in the community is infected with the virus is equal to x. In addition, y is a probability that an infected person tests positive and z is a probability that a non-infected person erroneously tests positive. Answer the following questions. 1. 2. Assume that y = 0.8 and z = 0.001. Find a probability that a person is actually infected with the virus when the person tests positive. Let the relationship between y and z be z = 0.001y² +0.0005 (0 ≤ y ≤ 1). Find y that maximizes the probability that a person is actually infected with the virus when the person tests positive.
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