over multiple points in time, at one point in time | ||
by measuring, by counting | ||
at each point, over an interval of points | ||
as incomplete, as complete | ||
all of the choices above | ||
none of the choices above |
Because the equations are too difficult | ||
Because we agreed not to use Calculus in this course | ||
Because it would be zero for any value of x | ||
Because it would 1.0000 for any value of x | ||
All of the choices above | ||
None of the choices above |
Because the PDF is used to determine the Z score | ||
Because we use the CDF to calculate probabilities | ||
Because we must keep in mind that our calculations will be wrong to some extent if the shape of our data distribution differs from the shape defined by the PDF of the model we are using | ||
Because we could never remember the calculus involved in finding the area under a curve defined by the PDF | ||
All of the choices above | ||
None of the choices above |
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2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)
Suppose that U is a random variable with a uniform distribution on (0,1). Now suppose that f is the PDF of some continuous random variable of interest, that F is the corresponding CDF, and assume that F is invertible (so that the function F-1 exists and gives a unique value). Show that the random variable X = F-1(U) has PDF f(x)—that is, that X has the desired PDF. Hint: use results on transformations of random variables. This cute result allows...
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