The volume of a cone can be determined by summing up the infinitesimal circular cross-sections of the cone across the length of the cone Consider the function f(x) = x2 for x contained in [0,1].

Now consider an infinitesimal circular cross-sectional element of width dx and radius r = f(x) Determine the volume of the cone enclosedby the function f(x) by considering the volume of each circular cross-sectional element (Recall thatthe sum of infinitesimal elements can be represented as an integral Recall also that the area of a

circle is
A)

B)

C)

D)
1

Let X be a continuous random variable with probability density function f(x) that is defined over all real numbers.
DefineE[g(X)]whereg(x)is a continuous function.
A)

B)

C)

D)

Identify which of the following statements is true,where X is a discrete random variable that exists over the domain [a. b], and F(x) is its distribution function.
A)

B)

C)

D)

Consider the three vectors:

Determine which of (he vectors or combination of vectors shown in the options has the greatest magnitude

Identify which of the following statements are true.
I.Skewness measures how peaked a set of data is
II.Skewness is a measure of asymmetry of the distribution of the data about its mean.
III. For a symmetrically distributed data, the mean equals the median but not necessarily the mode IV. The value of a measure of skewness can be positive, zero or negative.