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Consider generalizing the problem of constant propagation to that of range analysis. For each variable, we wish to associate a minimum and maximum value, such that the actual value of the variable (at that site in the program) at runtime is guaranteed to fall between the two values. For example, consider
the following program.
After their assignment, variable x has range 5 _ _ _5 and variable y has range 3 _ _ _ 3. The effect of Step 14 gives z the range 8 _ _ _ 8. The effect of Step 15 gives z the range 2 _ _ _ 2. The assignment for w therefore gets the range 2 _ _ _ 8.
(a) Sketch the data flow lattice for a single variable. Be specific about the values for or .
(b) Is this a forwards or backwards propagation problem?
(c) If the variable v could have range r1 or r2, describe how to compute the meet of these two ranges.
Compute the proportion p (hat) for your sample Show your computation. Find a 95% confidence interval for p. What is the margin of error in this confidence interval? What is the meaning of this interval with respect to your data and project?
What is the probability that a randomly selected player bats over 0.300? What is the probability that a team of 25 players has a mean that is above 0.275?
A SRS of size 16 drawn from a Normally Distributed population has a mean of 30 and a standard deviation, s, of 5. With 95% confidence, what is the interval that captures the true mean of the population?
The formula for a 95% confidence interval yields the interval 640 ± 5.88. Find out whether each of the given statements is true or false.
the average income tax refund for 2009 tax year was 3095. assumes the refund per person follows the normal probability
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Suppose that the incumbent has sufficient capacity such that at p = w she can produce the market demand. If the price postentry is w, would an entrant enter? Should the price postentry reflect w? Equal w?
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