How to read these formulas correctly

How to read these formulas correctly

Hi! Im a begginer in learning english-speakin math, cause its not my native language. I really need your help to find out how to read these formulas (look the files) correctly, cause I have to prepare some kind of talk in front of big audience.

Thank you!
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Amiron313

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Re: How to read these formulas correctly

The first one says that "the probability that the random variable, X, is greater than or equal to $$x_c$$ and less than or equal to $$x_d$$ is equal to the sum, from i= c to i= d of $$f(x_i)$$ and that is equal to the sum, from i= c to i= d of $$\frac{1}{n}$$". That last equality is a bit peculiar. It says that $$f(x_i)= \frac{1}{n}$$, a constant, for all i. Because of that all three sums are $$\frac{1}{n}(d- c)$$.

The second says that "The probability that the random variable, x, is greater than or equal to c and larger than or equal to d is the integral, from x= c to x= d of f(x) with respect to x and that is equal to the integral, from c to d, of $$frac{1}{b- a} dx$$ which is equal to the fraction $$\frac{d- c}{b- a}$$. That is, the function, f(x), is the constant function, $$f(x)=\frac{1}{b-a}$$". Of course, because $$\frac{1}{b- a}$$ is a constant, the integral is $$\int_c^d \frac{1}{b- a}dx= \frac{1}{b- a}\int_c^d dx= \frac{1}{b-a}(d- c)= \frac{d- c}{b- a}$$.

The third says that "the function f(x) is equal to the constant $$\frac{1}{b- a}$$ as long as x is larger than or equal to a and less than or equal to b and equal to 0 for any other x (less than a or larger than b)."

HallsofIvy

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