Math Answers

Assume that the function y(x) = f (x) + g(x) has a single local minimum in the

interval 0 <= x <= 1, at x = xm. Write

(i) a function M-file (called funct.m) and

(ii) a MATLAB statement (using the fminbnd command)

that together will compute xm and the value of y at xm.

Let the continuous r.v. X denote the weight (in pounds) of a package. The range of weight of packages is

between 45 and 60 pounds.

(a) Determine the probability that a package weighs more than 50 pounds.

(b) Find the mean and the variance of the weight of packages.

Is there a continuous function f:[0,1]~>[0,1] that is not constant in any nontrivial interval such that f^-1{0} is uncountable?

Find the area under the standard normal distribution curve.

1. Between z = 0 and z = 1.66

2. Between z = 0 and z = -0.35

3. To the right of z = 1.10

4. To the left of z = -0.48

5. Between z = 1.23 and z = 1.90

6. Between z = - 1.56 and z = -1.83

7. To the left of z = - 2.15 and to the right of z = 1.62

8. To the left of z = 2.11

9. To the right of z = -0.15

10. To the right of z = 1.92 and to the left of z = 0.44

Let x be Bin(n,p). Find the mean square error of the p parameter estimator

R^3 is a inner product space over the inner product

<(x1,x2,X3),(y1,y2,y3)> = x1y1+ x2y2 - x3y3

True or false with full explanation

Suppose you want to encode messages containing only the following characters with their given respective frequencies: B: 55 D: 15 E: 80 G: 5 U: 45

(a) What is the minimum length bit string required to encode each character with a distinct, fixed-length code?

(b) Construct the Huffman Tree for the characters with the given frequencies. (Use the convention that when merging two vertices, the vertex with the largest count goes on the left.)

(c) Use your Huffman Tree to decode the message M = 00101010000011

(d) How many bits are required to encode the characters with the given frequencies using the Huffman Encoding and the fixed-length encoding you found in part (a)? How much storage savings does this represent?

Evaluate the following functions in differential operator form.

1. D(x²+2x-3) Ans. (2x+2)
2. D²(xe^3x-e^4x) Ans. 9xe^3x+6e^3x-16e^4x

Change the following point from polar to rectangular coordinate.

(3/2, n/12)

II. Evaluate f²(3ײ- 6x ‐2)dx

A small factory producing a single product has weekly fixed costs of production of $2,112 and weekly variable costs of $52x + 3/4 x2, where x is the quantity produced. the capacity of the factory is about 600 units.

Past experience suggests that the product’s price and quantity are linked by the following demand equation: p = 200 - 1/4 x (p, x > 0) where p = $ price/unit and x = quantity sold. You are required to:

(a) Find the level of production at which revenue is maximized

(b) Find any break-even points