- 7 Points What Can Be Interpreted As A Center Of Gravity Of The Random Variable S Pmf Mean Variance Standard Deviation S 1 (59.24 KiB) Viewed 72 times
7 points What can be interpreted as a center of gravity of the random variable's PMF: mean variance standard deviation skewness The second central moment is: 7 points standard deviation skewness mean variance A measure of the dispersion of RV X that has the same units as X is: 6 points skewness variance mean standard deviation The expected value or mean of a continuous random variable X is defined 7 points by: = a) E[X] = 19(x)fx(x)dx; b) EX) = 2xx"Px(x); c) E[X] = L xfx(x)dx; d) E[X] = [(x – E[X])?fx(x)dx. = a
The variance var(x) of a continuous random variable X is defined by: 8 points a) var(x) = E[(X – E[x])?); b) var[CX] = C var[X], where C constant; c) var(x) = (x - E[X])?fx(x)dx; d) var(X) = E[X2] - (E[X])? a с d The value x at which its probability mass function takes its maximum value 7 points is: the median of a discrete probability distribution the mode of a discrete probability distribution the excess kurtosis the sample mean Which from the listed below statements are true: 8 points kurtosis is a measure of the "peakedness of the probability distribution of a real- valued random variable if the mass of the distribution is concentrated on the right of the figure we have negative skew if the distribution is unimodal, then the mean=median-mode the median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one
Problem 1. X is a random variable with E(X) = 100 and var(X) = 15. Find (a) E(X2); (b) E(3x + 10); (c) E(-X); (d) var(-X); (e) 0x(-X). Solution: - Problem 2. Find expectation, variance, and standard deviation of discrete RV X of number of failures of the router during the day, if: P(X = 0) = 0.05, P(X = 1) = 0.1, PCX = 2) = 0.5, P(X = 3) = 0.3, P(X = 4) = 0.05. Solution: Problem 3. Let X be uniformly distributed on the interval [0; 1). Find expectation and variance of X. Continuous uniform RV has a PDF: fx(x) = b-a O otherwise. aif a sxsb, Solution: