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1. Prove that every complete, irreflexive, and transitive relation is asymmetric: if
x ≠ y, then x > y if and only if yx.
2. Prove that the Gale-Shapley algorithm for finding a stable matching satisfies the following property: if Cleopatra asks Mark to stay in front of her house at stage k, and at a later stage she asks Julius to stay in front of her house, then she prefers Julius to Mark.
consider the game where two dice die a and die b are rolled. we say that die a wins and write a gt b if the outcome of
The random variable X has the cumulative distribution function F(x) whose value or derivative F(x) is shown below for various values of x.
A machine produces 3 inch nails. A sample of 100 nails is selected, and it is found that 25 are shorter than 3 inches. Find the 95% confidence interval on the proportion of all such nails that are shorter than 3 inches.
the survival rate during a risky operation for patients with no other rate of survival is 76. what is the probability
telephone marketers and opinion polls use random digit dialing equipment to call residential telephone numbers at
Is there a significant difference in the average prices for these two different supermarket chains? Test at α = 0.05
Based on these results, what is the probability of a boy born to a couple using MicroSort's YSORT method? Does it appear that the technique is effective in increasing the likelihood that a baby will be a boy
In Excel, which of the following functions is used to conduct a hypothesis test (using the p -value) for a population variance
the probability that a small business will go bankrupt in its first year is 0.21. For 50 such small business, find the following probabilities by using either the binomial probability formula or by using the normal approximation.
In determining automobile mileage ratings, it was found that the mpg ( X ) for a certain model is normally distributed, with a mean of 30 mpg and a standard deviation of 1.5 mpg. Find the following:
Given that R2 = 0.31, complete the ANOVA table. State conclusion about the regression relationship. Testing Hypothesis about the coefficients b3, b4, using alpha = 0.05.
Determine the value of d for which the percentage of hunting is too large to sustain the population - Sketch a slope field with various initial populations (a portrait) for case of 10% hunting.
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