Question

All parts please. I think I have a and b but want to check once I am done.

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 2 140; a "negative" (event Tis X 110; the test is considered ambiguous (event T) 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 fxx b) Calculate the conditional probabilities P(T+H) and P(T H (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

ola tio K- 90 2.D 20 及。 но

Ti thr pseis havin blood Jua level C he ch Per.the Chub yule have Solveol 良3ub pot.f for remainins