lab05

lab05.R

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+# Q1 Write a function, hasAntibodies(n) that simulates checking n people and 
+# returns the number with antibodies. Assume people being checked are 
+# independent and that person has a 5% chance of having antibodies.
+hasAntibodies = function(n)
+{
+  hasAntibody    <- sample(c(0, 1), n, replace=TRUE, prob=c(0.5, 0.5))
+  sumHasAntibody <- sum(hasAntibody == 1)
+
+    return(sumHasAntibody)
+}
+
+# Q2 Write a function called truePositives(n) that simulates testing n people 
+# who have COVID-19 antibodies, and returns the number that test positive. Run 
+# your function for n=100000 and give your output.
+truePositives = function(n)
+{
+  isPositive    <- sample(c(0, 1), n, replace=TRUE, prob=c(0.1, 0.9))
+  sumIsPositive <- sum(isPositive == 1)
+  
+  return(sumIsPositive)
+}
+
+# Q4 Write a function called falsePositives(n) that simulates testing n 
+# people who do not have COVID-19 antibodies, and returns the number who test 
+# positive
+falsePositives = function(n)
+{
+  isNegative       <- sample(c(0, 1), n, replace=TRUE, prob=c(0.08, 0.92))
+  sumFalsePositive <- sum(isNegative == 0)
+
+  return(sumFalsePositive)
+}
+
+# Q7 Write a function called probNegativeGivenTestsNegative(n) that
+# simulates testing n samples and returns the following proportion:
+# num people without covid-19 antibodies who test negative /
+# total number of people who test negative
+probNegativeGivenTestsNegative = function(n)
+{
+  numWith    <- hasAntibodies(n)
+  numWithout <- n - numWith
+  
+  trueNumWith <- truePositives(numWith)
+  falseNeg    <- numWith - trueNumWith
+  
+  falsePos    <- falsePositives(numWithout)
+  trueNeg     <- numWithout - falsePos
+  
+  return(trueNeg / (trueNeg + falseNeg)) 
+}
+
+# Q8 write a function called probPositiveGivenTestsPositive(n) to get an 
+# answer to the following question: suppose our test is positive – that is, 
+# our test tells us that the person has COVID-19 antibodies. What is the 
+# probability that our test is correct – that is, the person actually has 
+# COVID-19 antibodies?
+probPositiveGivenTestsPositive = function(n)
+{
+  numWith    <- hasAntibodies(n)
+  numWithout <- n - numWith
+  
+  truePos <- truePositives(numWith)
+  falsePos <- falsePositives(numWithout)
+  
+  return(truePos / (truePos + falsePos))
+}
+