Consider a simple linear regression model with nonstochastic regressor: Yi = β1 + β2Xi + ui . 1. [3 points] What are the assumptions of this model so that the OLS estimators are BLUE (best linear unbiased estimates)? 2. [4 points] Let βˆ 1 and βˆ 2 be the OLS estimators of β1 and β2. Derive βˆ 1 and βˆ 2. 3. [2 points] Show that βˆ 2 is an unbiased estimator of β2.

Java program

Prime Numbers

A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2, 3, 5 and 7.

Write a java program which reads a list of N integers and prints the number of prime numbers in the list.

Input: The first line contains an integer N, the number of elements in the list.

N numbers are given in the following lines.

Output: Print the number of prime numbers in the given list.

Constraints:

1 ≤ N ≤ 10000

2 ≤ an element of the list ≤ 10⁸

Sample Input 1

5
2
3
4
5
6

Sample Output 1

3

Sample Input 2

11
7
8
9
10
11
12
13
14
15
16
17

Sample Output 2

4

For each of the three independent situations below determine the amount of the annual lease payments. Each describes a finance lease in which annual lease payments are payable at the beginning of each year. Each lease agreement contains an option that permits the lessee to acquire the leased asset at an option price that is sufficiently lower than the expected fair value that the exercise of the option appears reasonably certain. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.)

Determine the annual lease payments for each situation (Round your intermediate and final answer to the nearest whole dollar amount.):

One of New England​ Air's top competitive priorities is​ on-time arrivals. Quality VP Clair Bond decided to personally monitor New England​ Air's performance. Each week for the past 30​ weeks, Bond checked a random sample of 100 flight arrivals for​ on-time performance.

a)   Using a 95% confidence level, plot the overall percentage of late flights ( p ) and the upper and lower control limits on a control chart.

b)   Assume that the airline industry’s upper and lower control limits for flights that are not on time are .1000 and .0400, respectively. Draw them on your control chart.

c)   Plot the percentage of late flights in each sample. Do all samples fall within New England Air’s control limits? When one falls out-side the control limits, what should be done?

d)   What can Clair Bond report about the quality of service?

(Please Screen shot the Excel if its in excel

Fill in the missing values in the table below given that , dy/dt = 0.8y - 2 .

You are given the joint probability distribution: (x+2y)/30 for x = 1, 2 and y = 2, 4.

Calculate Var(5X – 4Y).

3. Consider a project having the following activities, time, and cost:

                                                  Normal       Normal       Crash         Crash      Maximum

                        Immediate          Time         Cost         Time          Cost         Time

      Activity      Predecessors      (weeks)          ($)          (weeks)          ($)       Reduced

            a               none                  4            3,000             2            5,000            2

            b               a                        5            5,000             3            8,000            2

            c               a                        4            7,000             4            7,000            0

            d               b                        4            6,000             2            8,000            2

            e               c,d                     8            4,000             6            8,000            2

            f               c                        3            4,000             2            9,000            1

            g               e,f                      4            2,000             2            7,000            2

Assume partial crashing (not all maximum crashing time has to be used) is available.

1. Draw the network diagram. How long does project take using normal time?
2. Which activities should be crashed to reduce the completion time of the project by two weeks? How much is the additional cost? Show all work.

Consider a project having the following activities, time, and cost:

                                                  Normal      Normal      Crash         Crash         Maximum

                        Immediate         Time        Cost         Time         Cost             Time

      Activity      Predecessors      (weeks)          ($)         (weeks)          ($)         Reduced

            a               none                  4            3,000            2            5,000               2

            b               a                        5            5,000            3            8,000               2

            c               a                        4            7,000            4            7,000               0

            d               b                       4            6,000            2            8,000               2

            e               c,d                     8            4,000            6            8,000               2

            f               c                        3            4,000            2            9,000               1

            g               e,f                     4            2,000            2            7,000               2

Assume partial crashing (not all maximum crashing time has to be used) is available.

1. Draw the network diagram. How long does project take using normal time?
2. Which activities should be crashed to reduce the completion time of the project by two weeks? How much is the additional cost? Show all work.

The at rest pulse rate of 32 students were recorded. The dataset contains the following variables: (1) Gender, (2) Age, (3) Pulse Rate (beats per minute), (4) Ordinal scale for how good they think they are in shape (1 = poor, 5 = good), (5) Weight, (6) Height Is there evidence to suggest the typical pulse rate of males is less than females? Download/Display Data Gender Age Are you in shape? Pulse Rate (min) Weight Height (inches) Female 18 2 84 165 61 Male 18 5 53 170 69 Female 27 3 100 150 64 Male 21 3 80 170 72 Female 21 4 80 130 63 Male 20 3 52 190 73 Male 19 3 72 165 72 Male 20 3 92 270 71 Female 18 3 80 138 64 Female 18 4 80 168 65 Male 19 4 80 147 71 Female 27 3 144 194 65 Male 35 2 96 260 72 Male 32 2 68 220 69 Female 18 2 80 145 64 Male 18 4 52 140 68 Female 23 3 80 140 63 Male 18 3 68 250 74 Male 19 4 80 230 75 Male 21 4 64 135 69 Male 18 2 58 190 70 Female 19 4 68 112 63 Male 19 2 68 170 67 Female 35 2 76 219 66 Female 25 3 84 127 61 Male 21 3 72 175 70 Male 20 2 72 174 70 Female 19 1 72 150 70 Female 22 3 68 170 66 Female 23 2 84 192 71 Female 27 4 92 137 67 Female 27 4 92 137 67.

Refer to Table 3-2. Which of the following combinations of cheese and wine could France produce in 40 hours?