DTSA 5002 - Statistical Inference for Estimation in Data Science EXAM STUDY GUIDE 2026/2027 COMPLETE QUESTIONS WITH VERIFIED CORRECT ANSWERS || 100% GUARANTEED PASS NEWEST VERSION

DTSA 5002 - Statistical Inference for Estimation in Data Science EXAM STUDY GUIDE 2026/2027 COMPLETE QUESTIONS WITH VERIFIED CORRECT ANSWERS || 100% GUARANTEED PASS NEWEST VERSION 1. Probability Mass Function (PMF) - ANSWER f(x) = P(X=x) = {(1/2) if x=0, (1/2) if x=1, 0 if otherwise} 2. Bernouilli Distribution - ANSWER pdf=(pi^x) * (1-pi)^(1-x) E=pi VAR=pi(1-pi) 3. Geometric Distribution - ANSWER Let Y = the number of trials required to get the first success; pdf = ((1-p)^x) * p * I(x) 4. Probability Density Function (PDF) - ANSWER an equation used to compute probabilities of continuous random variables 5. PDF Properties - ANSWER 1.) f(x) = 0 , 2.) Integral (-inf, inf) f(x) dx = 1 6. normal distribution - ANSWER A function that represents the distribution of variables as a symmetrical bell-shaped graph. 7. Exponential Distribution - ANSWER A probability distribution associated with the time between arrivals; lambda*exp(-lambda*x) 8. (R code) Probability that at standard normal is = 'x' - ANSWER pnorm(x) 9. Central Limit Theorem - ANSWER As the size n of a simple random sample increases, the shape of the sampling distribution of x̄ tends toward being normally distributed. 10. True or False: Consistent estimation means convergence in probability - ANSWER True 11. Asymptotic efficiency - ANSWER lim(n inf)(CRLB(theta)/Var[theta^])=1 12. confidence interval - ANSWER the range of values within which a population parameter is estimated to lie 13. R code: qnorm(level+(1-level)/2) - ANSWER returns the normal distribution (critical value) of a given confidence interval 14. critical value - ANSWER The dividing point between the region where the null hypothesis is rejected and the region where it is not rejected. 15. chi-squared distribution - ANSWER the distribution of the sum of m squared independent standard normal random variables 16. t distribution - ANSWER A distribution specified by degrees of freedom used to model test statistics for the sample mean, differences between sample means, etc. where IT (' s) is (are) unknown 17. R code: qt(level+(1-level)/2, n-1) - ANSWER returns criticial value for t distribution 18. pooled variance - ANSWER A weighted average of the two estimates of variance—one from each sample—that are calculated when conducting an independent-samples t test. 19. R code: rnorm() - ANSWER Generates a random number from a normal distribution 20. R code: () - ANSWER Returns a confidence interval for the difference b/t means 21. True or False: p^ lives between 0 and 1 - ANSWER True 22. Radiation from a Cesium-137 source is measured using a scintillation detector. The detector absorbs the radiation and re-admits the energy as visible photons at a certain rate commensurate with the half-life of Cesium 137. Which of the following distributions may be used to best describe the number of photons emitted during a one hour period of time? - ANSWER Poisson