### Probability and Statistical Analysis in Medical Diagnosis#### (a) Calculation of ProbabilitiesTo find the values of \(P(D)\), \(P(T)\), and \(P(D \cap T)\), we have the following:- \(P(D) = 0.168\) ✔️- \(P(T) = 0.394\) ✔️- \(P(D \cap T) = 0.076\) ✔️These values denote the probabilities of different events:- \(P(D)\): Probability of a change in diagnosis.- \(P(T)\): Probability of a change in treatment.- \(P(D \cap T)\): Joint probability of a change in both diagnosis and treatment.#### (b) Constructing a Hypothetical TableUsing the given probability information, we can set up a hypothetical table for a sample size of 1,000. The table will have columns corresponding to \(D\) and \(D^C\) (change in diagnosis and no change in diagnosis, respectively) and rows corresponding to \(T\) and \(T^C\) (change in treatment and no change in treatment, respectively). Below is the table template:| | Change in Diagnosis (\(D\)) | No Change in Diagnosis (\(D^C\)) | Total ||-------------------------------|-----------------------------|-----------------------------------|-------------------|| Change in Treatment (\(T\)) | x | y | || No Change in Treatment (\(T^C\)) | z | w | || Total | | | 1,000 |- \(x\): Count of cases with a change in both diagnosis and treatment.- \(y\): Count of cases with a change in diagnosis but not in treatment.- \(z\): Count of cases with no change in diagnosis but a change in treatment.- \(w\): Count of cases with no change in both diagnosis and treatment.It is important to note that this table helps visualize and calculate probabilities for combined events and can aid in medical decision-making processes based on diagnostic and treatment probabilities.

From the given information, P(D)=0.168, P(T)=0.394 and P(D∩T)=0.076.

Answered: (b) Use the given probability…

MATLAB: An Introduction with Applications

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Author:Amos Gilat

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(b) Use the given probability information to set up a hypothetical 1,000 table with columns corresponding to D and DC and rows correspondir Change in Diagnosis (D) No Change in Diagnosis (DC) Total Change in Treatment (7) No Change in Treatment (7) Total X X X 1,000