MATH/STAT 394: Probability I Wellner, 1/3/2000

Math Diagnostic Quiz

1.

$1 + 2 + 3 + \cdots + 30 =$

2.

$1 + 2 + 3 + \cdots + m =$

3.

$1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \frac{1}{81} + \cdots =$

4.

$\sum_{n=0}^{\infty} x^n =$

5.

$\int_1^2 x^3 dx =$

6.

$\frac{d}{dx} (x^2 \log x) =$

7.

$\frac{d}{dx} (\cos(x^3)) =$

8.

Sketch the graph of the function x² e^-x for x > 0 and find its maximum value.

9.

Sketch the graph of the function f(x) = x² + 5x +2 for $-\infty < x < \infty$, find its minimum value, and find the roots of the equation f(x) = 0.

10.

$\int_0^1 \int_0^1 x^2 dx dy =$

11.

Let T be the triangle with vertices (0,0), (1,0), and (1,1) in the x-y plane. Then $\int\int_T y dx dy =$?

12.

How many distinct unordered subsets can be formed from $\{ 1, 2, \ldots , n \}$?

13.

In how many distinct ways can the integers $1, \ldots , n$ be arranged? (i.e. how many permutations?)