core: 0 of 1 pt HW Sco 3.6.90 In a study, the various stages of sleep for a larg

Question

core: 0 of 1 pt HW Sco 3.6.90 In a study, the various stages of sleep for a large group of people were monitored in 30 the results the table gives the number of epochs that ocourred when transitioning from the t ourrent sleep stage. Complete partsa (Type an integer or a decimal. Round to three decimal places as needed.) The probability is 0.953 c. Are the events (previous stage is Non-REM) and (ourment stage is REMI mutually exclusive? Select the comect choice below and f probability that the previous sleep stage was not the REM sta Non-REM 30,536 163 1,554 311 7570 128 44 5.548 REM Wake1,492 (Type an integer or a decimal. Round to three decimal places as needed.) Print Done B. No, because P(previous stage is Non-REM)- and Ploument stage is REM)- C. Yes, because P(previous stage is Non-REM)- and P(curmrent stage is REM) D. Yes, because P(previous stage is Non-REM n (arrent stage is REM»- (Type an integer or a decimal. Round to three decimal places as needed.) A. No, bease Plament stage is Wake) {previous stage is Non-REM)-l and Parema stage is Non-REM). . No, because Pep ovou s st ge nun REM){cumen stage is wakelje o. Yes, because Pte mere stage is wake) I previous stag. Non-REM). and P previous stage is Non-REM)- and Pprevious stage is Non-REM).

Explanation / Answer

From the given problem we can construct the following table

1.previous sleep stage for the epock was the wake state, what is the probability that the current sleep stage is wake= P(A3/B3) = P(A3 and B3)/P(B3) =5548/7230= 0.767

2.Current sleep stage for the epoch is wake, what is the probability that the present sleep stage was not the rem= 1- P(B2/A3) =1- [ P(B2 and A3)/ P(A3)] = 1 - [344/7384]=1 - 0.0465=0.953

3. Are the events previous stage is non rem and current stage is rem are mutually exclusive

ans) A NO

P(B1 and A2 ) = 311/47646 = 0.007 is not equal to 0

hence B1 and A2 are not mutually exclusive

Note.. If P(B1 and A2) = 0 then B1 and A2 are mutually exclusive

4. Are the events previous stage is non rem and current stage is wake are independent

ans) C No

P(previous stage is non rem / current stage is wake )= P(B1 / A3) =1492/7384=0.202 and is not equal to P(B1)=1492/32339=0.046

Hence the answer is C

Note. B1 and A3 are said to be independent if P(B1 / A3) = P (B1)

but in the given problem P(B1/A3) is not equal to P(B1)

Current stage(A) Previous stage(B) Non rem (B1) Rem (B2) Wake(B3) Total Non rem (A1) 30536 163 1554 32253 Rem (A2) 311 7570 128 8009 Wake (A3) 1492 344 5548 7384 Total 32339 8077 7230 47646

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