Probability and Frequency GMLE Practice Questions (Page 9)

Questions 41–45

1. 41foundation · easy

   Which of the following is a property of a discrete probability distribution?

   • AThe probability of any single point is zero
   • BThe distribution is always symmetric
   • CThe random variable can take any value in an interval
   • DThe sum of all probabilities equals 1
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2. 42foundation · easy

   A medical test for a disease has a false positive rate of 5% and a false negative rate of 1%. The disease prevalence is 2%. Using Bayes' theorem, which quantity is directly updated by the test result?

   • AThe sensitivity of the test
   • BThe prior probability of the disease
   • CThe false positive rate of the test
   • DThe posterior probability of the disease given the test result
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4. 43foundation · easy

   Bayes' theorem is used to:

   • ACalculate the probability of two independent events occurring together
   • BDetermine the expected value of a random variable
   • CMeasure the spread of a probability distribution
   • DUpdate the probability of a hypothesis based on new evidence
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5. 44application · medium

   A financial analyst is comparing two investment portfolios. Portfolio X has an expected annual return of 8% with a standard deviation of 15%. Portfolio Y has an expected annual return of 8% with a standard deviation of 10%. Which portfolio is considered less risky based on this information?

   • ABoth portfolios have the same risk because they have the same expected return.
   • BRisk cannot be determined from standard deviation alone.
   • CPortfolio X, because it has a higher standard deviation.
   • DPortfolio Y, because it has a lower standard deviation.
   Reveal Solution Discussion Select an answer first
6. 45expert · hard

   A data scientist is comparing two probability distributions for a random variable that represents the daily number of website visits. Distribution A is Poisson with λ=100. Distribution B is normal with mean=100 and standard deviation=10. Which statement is true?

   • AThe expected values are the same, but the variances cannot be compared because the distributions are different types.
   • BDistribution B has a higher variance than Distribution A.
   • CBoth distributions have the same expected value, but Distribution A has a variance of 100 and Distribution B has a variance of 100.
   • DDistribution A has a higher expected value than Distribution B.
   Reveal Solution Discussion Select an answer first