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Apparently f(x)=sqrt(x)

But I'm not sure why. That's what I'm looking for now :)

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Q: What is an example of uniform continuous but not lipschitz continuous function?
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Uniform distribution and moment generating function?

See: http://en.wikipedia.org/wiki/Uniform_distribution_(continuous)


What are the characteristics of continuous distribution?

The probability distribution function (pdf) is defined over a domain which contains at least one interval in which the pdf is positive for all values. Usually the domain is either the whole of the real numbers or the positive real numbers, but it can be a finite interval: for example, the uniform continuous distribution. Also, trivially, the pdf is always non-negative, the integral of the pdf, over the whole real line, equals 1.


In Excel what function will give you an estimate of the value of a continuous random variable if you know the probability of that variable?

There are infinitely many continuous probability functions and there is no information whatsoever in the question to determine the nature of the distribution: uniform, Normal, Student's t, Chi-square, Fisher's F, Gamma, Beta, Lognormal, etc, etc. Second, every continuous function must have at least two points for which the probability is the same. There is no information as to which of these two (or more) points is the relevant one. There can therefore be no answer.


What is the probability of choosing a number greater than 21 if a number is randomly chosen between 1 and 50?

Assuming the uniform continuous distribution, the answer is 29/49. With the uniform discrete distribution, the answer is 29/50.


Is the graph for nonuniform motion a curve line?

No. First of all, it depends on what is being graphed. Also, a distance-time graph of non-uniform motion could be any continuous line other than a straight line - for example a saw-tooth shape.