**Testing Independence of Events C and D**Examine the pair of events C and D for independence using the following table:| | A | B | C | Total ||---|-----|-----|-----|-------|| D | 0.18| 0.02| 0.20| 0.40 || E | 0.06| 0.10| 0.04| 0.20 || F | 0.06| 0.08| 0.26| 0.40 || Total | 0.30| 0.20| 0.50| 1.00 |**Determining Independence**Are C and D independent or dependent and why? Select the correct answer below and fill in the answer boxes to complete your choice.**Options:**- **A.** C and D are dependent because P(C∩D) does not equal P(C)P(D). P(C∩D) = [ ], and P(C)P(D) = [ ]. - **B.** C and D are independent because P(C∩D) does not equal P(C)P(D). P(C∩D) = [ ], and P(C)P(D) = [ ]. - **C.** C and D are dependent because P(C∩D) equals P(C)P(D). P(C∩D) = [ ], and P(C)P(D) = [ ]. - **D.** C and D are independent because P(C∩D) equals P(C)P(D). P(C∩D) = [ ], and P(C)P(D) = [ ].**Explanation:**- **P(C∩D):** This represents the probability of both events C and D occurring simultaneously.- **P(C):** This represents the probability of event C occurring.- **P(D):** This represents the probability of event D occurring.To determine if events C and D are independent, fill in the probabilities to check if P(C∩D) equals P(C)P(D). If they are equal, the events are independent. If not, they are dependent.

Test the pair of events C and D for independence based on the following table. A B 0.18 0.02 D E Total 0.06 0.06 0.30 0.10 0.08 0.20 C 0.20 0.04 0.26 0.50 Total 0.40 0.20 0.40 1.00 and P(C)P(D)= Are C and D independent or dependent and why? Select the correct answer below and fill in the answer boxes to complete your choice. O A. C and D are dependent because P(COD) does not equal P(C)P(D). P(CND)= O B. C and D are independent because P(COD) does not equal P(C)P(D). P(CND)= and P(C)P(D)= OC. C and D are dependent because P(CND) equals P(C)P(D). P(COD)= and P(C)P(D)= OD. C and D are independent because P(CND) equals P(C)P(D). P(CND)= and P(C)P(D)=

Test the pair of events C and D for independence based on the following table. A B 0.18 0.02 D E Total 0.06 0.06 0.30 0.10 0.08 0.20 C 0.20 0.04 0.26 0.50 Total 0.40 0.20 0.40 1.00 and P(C)P(D)= Are C and D independent or dependent and why? Select the correct answer below and fill in the answer boxes to complete your choice. O A. C and D are dependent because P(COD) does not equal P(C)P(D). P(CND)= O B. C and D are independent because P(COD) does not equal P(C)P(D). P(CND)= and P(C)P(D)= OC. C and D are dependent because P(CND) equals P(C)P(D). P(COD)= and P(C)P(D)= OD. C and D are independent because P(CND) equals P(C)P(D). P(CND)= and P(C)P(D)=

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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