For n > 3 fZn (z) can be approximated analytically or numerically. An analytical approximation for fZn (z) can be based on the Central Limit Theorem which roughly states that Zn approaches a Gaussian random variable with mean 0 and variance 1 as n → [infinity] (see p. 369-370 in the text for a precise statement and discussion). Hence a Gaussian pdf with mean 0 and variance 1 can be used to estimate the pdf of Zn. A numerical approximation for fZn (z) can be based on a simulation. Generate n × K realizations of a uniform random variable on (0, 1), and denote them by {xi, k : i = 1, . . . , n; k = 1, . . . , K} . {xi, k : k = 1,

The table shows the relationship between the number of cups of cereal and the number of cups of raisins in a cereal bar recipe: number of cups of cereal number of cups of raisins 8 2 12 3 16 4 molly plotted an equivalent ratio as shown on the grid below: a graph is shown. the title of the graph is cereal bars. the horizontal axis label is cereal in cups. the x-axis values are 0, 20, 40, 60, 80,100. the vertical axis label is raisins in cups. the y-axis values are 0, 10, 20, 30, 40, 50. a point is plotted on the ordered pair 40,20. which of these explains why the point molly plotted is incorrect? (a) if the number of cups of cereal is 40, then the number of cups of raisins will be10. (b)if the number of cups of raisins is 40, then the number of cups of cereal will be10. (c) if the number of cups of cereal is 40, then the number of cups of raisins will be 80. (d) if the number of cups of raisins is 40, then the number of cups of cereal will be 80.