You toss a biased coin with the probability of heads as p. (a) What is the expected number of tosses required until you obtain two consecutive heads ? (b) Compute the value in part (a) for p = 1/2 and p = 1/4.

1) Data for a notes receivable made on May 15th is as follows: Notes Receivables $30,000 Number of days for the note 120 Interest rate 4% Required: (1) Find the maturity date (2) Find the maturity value of the note.

Use power series approximations method to approximate the solution of the initial value problem: y"− (1+ x) y = 0 y(0) = 1 y'(0) = 2 (Write all the terms up to the power ). x^4

Draw a MPLS diagram with the following requirements:1. 10 IPv6 routers: 4 routers in one segment, 3 routers in second segment, 1 router to connect these two segments

2. Explain MPLS operation in above network.

Draw a MPLS diagram with the following requirements:1. 10 IPv6 routers: 4 routers in one segment, 3 routers in second segment, 1 router to connect these two segments

2. Explain MPLS operation in above network.

1- Pick 3 favorite thermal engine cycles

2- Draw PV diagram for each (label each step in the cycle)

3- Give >1 example of an application for each engine

4- Calculate work for each engine

Use Lagrange interpolation to find the polynomial p3(x) of degree 3 or less, that agree with the following data: p3(−1) = 3, p3(0) = −4, p3(1) = 5, and p3(2) = −6.

Using python to solve

Bloomington Publishers is considering publishing five different textbooks. The maximum number of copies of each textbook that can be sold, the variable cost of producing each textbook, the sales price of each textbook, and the fixed cost of a production run for each textbook are given in the file Prob3. For example, producing and selling 2000 copies of book 1 yields a revenue of $80(2000) = $160,000 but costs $80,000 + $44(2000) = $168,000. This company can produce at most 20,000 copies in total. Furthermore, it can publish no more than three different types of textbooks. Also, it knows that it cannot publish book 1 if it chooses to publish book 2. Finally, if this company publishes book 4 it must also publish book 5. Bloomington Publishers wants to find a production plan that maximizes total profit. Formulate and solve an integer programming model in Prob3 to help this publisher identify the best production plan.

You draw the following ve numbers from a standard normal distribution:
f= (1:7; 0:55; 0:85)
What are the equivalent draws from a normal distribution with mean 0:8 and variance
25?
b. Suppose x1 ~ N(1; 5) and x2~ N(2; 2). The covariance between x1 and x2 is 1:3.
What is the distribution of x1 + x2 and x1 - x2?
c. Suppose x1 ~N(1; 5), x2 ~N(2; 3), and x3 N(2:5; 7), with correlations P1;2 = 0:3,
P1;3 = 0:1 and P2;3 = 0:4. What is the distribution of x1 + 2x2 - 3x3?

**CODED IN C LANGUAGE**

Case 1: The given snapshot in the assignment instructions checks for the following:

• P to be switched with Q (Once done will remain as it is in all the rows)
• If the user enters the same P again, the program must not make any changes

For instance, given elements are 0123456789

3 4          0              0124456789

2 5          1              0154456789 (Keeping the change in Row 0 (input for row 1); 2 is switched to 5)

1 6          2              0654456789 (Keeping the change in row1 (input for row 2); 1 has been replaced with 6)

This implies that for every other row, the input array elements get changed to its previous row elements.