Question

please answer questions a-d fully and show your work

5. A test for diabetes is a measurement of a person's blood sugar level, X, following an overnight fast. For a healthy person, a result in the range 70-110 mg/dl is considered normal. A "positive" for diabetes, (event T+) is X 140; a "negative" (event T) is X 110; the test is considered ambiguous (event TO) İf I 10 < X < 140 For a healthy person (event H) X is the Gaussian random variable with μ 90 and σ 20. For someone with diabetes (event D), X is Gaussian with μ = 160 and σ = 40. The probability that a randomly chosen person has diabetes is P(D) = 0.10, and P(H) = 0.90. (a) Determine the conditional PDF x (b) Calculate the conditional probabilities P(T H) and P(TH) c) Find P(HIT), the probability that a person is actually healthy, given the event of a negative test result. d) Calculate the probability that an ambiguous result is obtained.

Answer 1

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- O.2636

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