Suppose a [ 1 ] , a [ 2 ] , a [ 3 ] , .... a [ m ] is a one-dimensional arry and consider the following algorithm segment: s u m : = 0 for k :=1 to m s u m : = s u n + a ⌊ k ⌋ n e x t k Fill in the blanks below so that each algorithm segment performs the job as the one shown in the exercise statement. a. s u m : 0 for i : = 0 to_____ sum:=____ next i b. s u m : 0 for i : = 2 to_____ sum:=____ next j
Suppose a [ 1 ] , a [ 2 ] , a [ 3 ] , .... a [ m ] is a one-dimensional arry and consider the following algorithm segment: s u m : = 0 for k :=1 to m s u m : = s u n + a ⌊ k ⌋ n e x t k Fill in the blanks below so that each algorithm segment performs the job as the one shown in the exercise statement. a. s u m : 0 for i : = 0 to_____ sum:=____ next i b. s u m : 0 for i : = 2 to_____ sum:=____ next j
Solution Summary: The author explains how each algorithm segment performs the same job as the one shown in the exercise statement.
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1. The CLT provides an approximate sampling distribution for the arithmetic average Ỹ of a
random sample Y₁, . . ., Yn f(y). The parameters of the approximate sampling distribution
depend on the mean and variance of the underlying random variables (i.e., the population
mean and variance). The approximation can be written to emphasize this, using the expec-
tation and variance of one of the random variables in the sample instead of the parameters
μ, 02:
YNEY,
· (1
(EY,, varyi
n
For the following population distributions f, write the approximate distribution of the sample
mean.
(a) Exponential with rate ẞ: f(y) = ß exp{−ßy}
1
(b) Chi-square with degrees of freedom: f(y) = ( 4 ) 2 y = exp { — ½/ }
г(
(c) Poisson with rate λ: P(Y = y) = exp(-\}
>
y!
y²
2. Let Y₁,……., Y be a random sample with common mean μ and common variance σ². Use the
CLT to write an expression approximating the CDF P(Ỹ ≤ x) in terms of µ, σ² and n, and
the standard normal CDF Fz(·).
3. We'd like to know the first time when the population reaches 7000 people. First, graph the
function from part (a) on your calculator or Desmos. In the same window, graph the line y =
7000. Notice that you will need to adjust your window so that you can see values as big as
7000! Investigate the intersection of the two graphs. (This video shows you how to find the
intersection on your calculator, or in Desmos just hover the cursor over the point.) At what
value t> 0 does the line intersect with your exponential function? Round your answer to two
decimal places. (You don't need to show work for this part.) (2 points)
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