Suppose X and Y are continuous random variables with joint pdf f(x, y) = 24xy if 0 < x, 0 < y, and x + y < 1, and zero otherwise. (a) Find E(XY). (b) Find the covariance of X and Y. (c) Find the correlation coefficient of X and Y. (d) Find Cov(3X, 5Y). (e) Find Cov(X + 1, Y – 2). (f) Find Cov(X + 1, 5Y – 2). (g) Find Cov(3X + 5, X).

For a Gaussian discriminant classifier, where you model P(y = 1) (using a binomial) and P(x|y = 0) and P(x|y = 1). The latter have distinct means µ0 and µ1, and a shared covariance matrix Σ . If we classify an example for which we know inputs x1, . . . xn−1, but the value of xn is missing.  The value of xn is filled by its class-conditional means, E(xn|y = 0) and E(xn|y = 1). Using the log-odds ratio, can someone provide a mathematical justification

The grade point average of the students at UTC is 2.80 with a standard deviation of 0.84. The grade point average of students at UTK is 2.4 with a standard deviation of 0.84. Which university shows a more dispersed grade distribution?

A mathematics teacher recorded the length of time, y minutes, taken to travel to school when leaving home x minutes after 7 am on seven selected mornings. The results are as follows. x 0 10 20 30 40 50 60 y 16 27 28 39 49 48 51 a. plot the data on scatter diagram b. (i) calculate the equation of the least squares regression line of y on x, writing your answer in the form y = a + bc (ii) draw the regression line on your scatter diagram c. the mathematics teacher needs to arrive at school no […]

In an opinion poll, each individual in a random sample of 275 individuals from a large population is asked which political party he/she supports. If 45% of the population support party A, calculate (approximately) the probability that at least 116 of the sample support A.