Question

Can you please explain why each is true or not true and the final answer. Thanks!

A-2. We have the following four statements: a) The expected value and the mean of a random variable are the same. b) Normal distribution that is thinner and taller has a high variance. c) The 95% confidence interval for the true population mean u tells us that the random variable u falls within the confidence interval with probability 0.95. d) R squared is the proportion of variation in the dependent variable that has been explained by regression. How many of these statements are true? A. O B. 1 C. 2 C. 2 D.3 E.4

Answer 1

A-2 a) True. In discrete case If is random variable, then. EU = be P[X2] = mean In continuous case If x in a random variable, then E(X) = (e. foodse = mean. b False When the variance of normal distribution increases it become more Platter. That in the distribution has that much deviation from the Mean value

Graph of Normal distribution with different values of the parameter '$\sigma$'

— - — U=0, 0 =0.75 U=0, 0:1 U=0, 0=2

" True. A 95% confidence level means that if the experiment or survey were repeated 95% time the dala would match from the entor population. hey were repeated 95% of the 0.0251 0.025 lower lower X Upper limit d) R² is a statistical tool which measures the proportion of variance for a dependent variable y that are explained by indepenent variables (xs, in a regression model. So it is true. There are three true options- le D. 3