DTSA 5002 - Statistical Inference for Estimation in Data Science Comprehensive Resource To Help You Ace Exams Includes Frequently Tested Questions With ELABORATED 100% Correct COMPLETE SOLUTIONS Guaranteed Pass First Attempt!! Current Up

DTSA 5002 - Statistical Inference for Estimation in Data Science Comprehensive Resource To Help You Ace Exams Includes Frequently Tested Questions With ELABORATED 100% Correct COMPLETE SOLUTIONS Guaranteed Pass First Attempt!! Current Update!! 1. Probability Mass Function (PMF) - Correct Answer: f(x) = P(X=x) = {(1/2) if x=0, (1/2) if x=1, 0 if otherwise} 2. Bernouilli Distribution - Correct Answer: pdf=(pi^x) * (1-pi)^(1-x) E=pi VAR=pi(1-pi) 3. Geometric Distribution - Correct 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) - Correct Answer: an equation used to compute probabilities of continuous random variables 5. PDF Properties - Correct Answer: 1.) f(x) = 0 , 2.) Integral (-inf, inf) f(x) dx = 1 6. Normal distribution - Correct Answer: A function that represents the distribution of variables as a symmetrical bell-shaped graph. 7. Exponential Distribution - Correct Answer: A probability distribution associated with the time between arrivals; lambda*exp(-lambda*x) 8. Binomial Distribution - Correct Answer: a frequency distribution of the possible number of successful outcomes in a given number of trials in each of which there is the same probability of success.; (n x) * p^x * (1-p)^(n-x) * I{0,..,n}(x) Poisson Distribution - Correct Answer: Probability distribution for the number of arrivals during each time period; f(x) = (exp(-lambda)*lambda^x)/ x! * I{0, 1,...}(x) 9. Uniform distribution - Correct Answer: the frequency of each value of the variable is evenly spread out across the values of the variable; f(x) = 1/(b-a) * I(a,b)(x) 10. Gamma Distribution - Correct Answer: used to model waiting time until kth event occurs X~GAM(c,d) 0c 0d pdf: f(x)=1/[(c^d)gamma(d)] x^(d-1)e^-x/c 0x mean: dc variance: dc^2 MGF: Mx(t)=[1/(1-ct)]^d 11. Joint PMF - Correct Answer: f(x,y) = P(X=x, Y=y) 12. Marginal Probability - Correct Answer: the values in the margins of a joint probability table that provide the probabilities of each event separately 13. Expected value - Correct Answer: the average of each possible outcome of a future event, weighted by its probability of occurring 14. Expected value of normal distributions - - Correct Answer: MU 15. Expected value of exponential distribution - Correct Answer: 1/lambda 16. Law of the Unconscious Statistician - Correct Answer: integral(-inf, inf) (g(x)*fx(x))dx