Question

Question # A.5 (A) Suppose in a war-front, D denotes a threat-state and D refers to no threat- (safe) state. While taking necessary defensive decisions, there are two possible errors that may occur: Type I error means that the threat-free (safe) state (of D) is (wrongly) fault-alarmed as being D denoting the a threat-state; hence, a defensive action is pursued, which is indicated as the state, F). Further, a Type II error could occur whenever the state-of-threat (D) is (wrongly) miss-considered as non- threat (safe) state and such miss-consideration is depicted as state F and no defensive measure is undertaken. (a) Mark on the following state-diagram Type I and Type II errors mentioned above (b) Assume P(D) -0.005; probability (Type I error) -0.015 and probability (Type II error) 0.08; and P(F/D) - 0.995. Label all prior, joint and posterior the probabilities between (D.D) and ( F. F) as appropriate. Hence determine: (i) P(D); (ii) P(F); (iii) P(D/F); (iv) PD/F); and (v) P(D/F). [Use Bayes' theorem as needed] (e) Identify the following in (b) above: (i) The true-positive and true- negative probabilities, and, (ii) inverse probability depicting a true state that conditionally specifies unsafe condition predisposed to the underlying threat-state. [Answer hint: (ii) P(D/F) - 0.2356]

Answer 1

ANSWER a) eniven figore D f pe- error is given the state f B) bot e concouded so the aro Prom3to f pe-1 errow Tpe error is given the state of D, bot e conciu ded F, so the ano rom d to f is ype-T error. b Now assume P Cype Teror) 2 P CP/D) .015 P pe eorP (FID) O-08 P (th) O.95 P CID) - 1-P CFID) 1-0.08 0.92 17 Cs Scanned p(D) CamScar l-PCD) rd

PCD) 1-a005 2 0.09a the ous o total probabiliy PG PCD) PFID)+ (p Dp C? /) .O1958 and PF) pCf --0.619a5 P (F = ০:৭४०५१5 usingbayes eheoreny PCDIR)=PCPID) P (D)/P .98x 0-005 0.0195as 0.3356 PCDIP and P CDP) -0235 РOР) Scanned with 7644 CS CamScanner

sing boyes theoren P CD/FPFID) pC)/p () Oo8t0.005 0.9804 PCDIF) O.600 408 and P (D/F) -Р СDF) PC5IF P Cf/D) 9a PF ID) 1p(FID) 9Tue positwe 12 Tue Nogative - 0 OLS PCDIF) PD/F) a356 7 ०.१११ऽ१२ THE END- Scanned with CamScanner CS