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1a. If X and Y are infinite sets with the same number of elements, show that the following conditions are equivelent for a function f: X-->Y:
(i). f is injective(ii). f is bijective(iii) f is surjective
1b. Suppose there are 11 pigeons sitting in some pigeonhole. If there are only 10 pigeonholes prove that there is a hole containing more than one pigeon.
I just dont know where to begin with the proof and how to show this.
Five cards are drawn from an ordinary deck without replacement. Find the probability of getting:
At 0.05 level of significance, is there enough evidence to conclude that difference exists between proportion of students who have ear infections at one school and the other?
Insurance policy from company A costs $300 a year but guarantees to replace any losses due to theft. Create the decision tree.
A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighted on a very accurate scale. The results in grams were:
A previously used drug treatment has a mean remission time of 12.5 weeks. Does the data indicate that the mean remission time using the new drug is different from 12.5 week at a level of significance of 0.01?
Sun Love grapefruit growers have determined that the diameters of their grapefruits are normally distrubuted with a mean of 4.5 inches and a standard deviation of 0.3 inches.
Use the least-squares method to compute the regression of coefficients b0 and b1.
A manager wishes to find out whether there is a relationship between the number of radio ads aired per week and the amount of sales (in thousands of dollars) of a product. The data for the sample are shown below. a) Draw the scatter plot for the v..
Drawing the standard normal curve and indicating the area representing the probability and
Who are also athletes but who are not regularly hit in the heads. Is this an example of an experimental or a non-experimental study? Why?
What is the probability that at least one of the 40 shuttle missions scheduled over the next 5 years results in a critical-item failure?
Let X1,... x30 be independent Poisson random variables having mean 1. (a) Use Chebyshev's inequality to find a lower bound on the probability.
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