Part I:

1. Given that f(x) is a p.d.f. for random variable X, find a in terms of b.

2. Find the average of E[X] in terms of b.

3. Find the variance V [X] = E[(X - μ)²] = E[X²]-μ^2 in terms of b.

4. Given that the average is 10 find P(0 < x < 10). Give your answer as a percent accurate to two decimal places.

5. Graph the pdf for μ = 10.

6. Find the CDF for μ = 10 and graph it.

Part II:

Assume that a point in cartesian coordinates (x, y, z) is represented in paraboloidal coordinates as (u, v,w).

1. Give the gradient operator in paraboloidal coordinates.

2. What are h1, h2 and h3 in the paraboloidal coordinate system.

3. Given a vector r^-> = x^ i + y^ j + z^ k in cartesian coordinates, give the vector dr^-> that results from an innitesimal change in r^-> in paraboloidal coordinates. Write dr^-> as a linear combination of the three unit vectors used in the paraboloidal coordinate system.

Part III:

1. Given that the le data.txt contains only real numbers seperated by white space, write down a sequence of maple commands that will read the data into a maple list and then plot a histogram of the elements in the list. Make sure you close the le when you are nished. Your commands are correct if when typed exactly as given maple gives the correct results.