Show using the definition of expected values for discrete random variables (Eq. 5.1) that for a discrete random variable, X, E(g(X)) = ∑g(x) p(x) where g(x) is linear. That is, show the formula is true assuming that g(x) = ax + b. You are showing that a special case of Eq. 5.2 is true; therefore, you many not use that formula in the derivation. Submission type: Submit entries below as answer to receive credit Save entries below (not submitted for credit yet)

Which is a true statement comparing the graphs of x^2/6^2-y^2/8^2 = 1 and x^2/8^2-y^2/6^2 the foci of both graphs are the same points. the lengths of both transverse axes are the same. the directrices of = 1 are horizontal while the directrices of = 1 are vertical. the vertices of = 1 are on the y-axis while the vertices of = 1 are on the x-axis.

Suppose you just purchased a digital music player and have put 8 tracks on it. after listening to them you decide that you like 4 of the songs. with the random feature on your player, each of the 8 songs is played once in random order. find the probability that among the first two songs played (a) you like both of them. would this be unusual? (b) you like neither of them. (c) you like exactly one of them. (d) redo () if a song can be replayed before all 8 songs are played.

For g(x) = 5x - 3 and h(x) = [tex]\sqrt{x}[/tex], find (g · h)(4)