14. (20 pts) This data shows the number of healthcare worker injuries in a hospital over the last 24 months.

The mean is 6.292.

(a) Using Goodness-of-fit test for Poisson, test if the data follows the Poisson distribution and determine λ.

(b) Using the mean computed from (a), Compute the probability that there will be more than 7 injuries next year.

(c) Using the mean computed from (a), compute the probability that there will be 5 or fewer injuries next year

8) Match each definition with the term it defines. You may use terms once, more than once, or not at all. If all of your answers are correct, a clue will appear.

A. Variance
B Dependent
C. Residual plot
D. Independent
E. Mutually exclusive
F. Correlation coefficient G. Simple random sample H. Permutation
I. Z-score

J. Normal distribution
K. Student’s t distribution
L. Tukey-Kramer test
M. Discrete
N. Continuous
O. Skewed to the left
P. Chi-square goodness-of-fit test Q. Confidence Interval
R. One-way ANOVA

S. Combination
T. Binomial experiment U. Relative Frequency
V. Cumulative Frequency W. Null hypothesis
X. Alternative hypothesis Y. Skewed to the right
Z. Symmetric

____ A subset of a population in which each member of the population has an equal probability of being included

____ Two events are ______________ if they cannot occur at the same time.

____ Experiment with a fixed number of independent trials, each with exactly 2 outcomes and the same probability of success

____ Used to test the hypothesis that several population means are all equal

____ The number of standard deviations that a value falls above or below the mean

____ Two events are ______________ if the occurrence of one does not affect the probability of the other.

____ If x̄ is much smaller than the median, the distribution is most likely this shape.

____ Numerical measure of the strength and direction of a linear relationship between two variables

____ When two variables have a linear relationship, the ____________ will not exhibit any noticeable pattern.

____ The number of ways that a group of items can be ordered

____ ? − ? ?

____ A collection of objects in which the order doesn't matter
____ A range of values that is likely to include an unknown parameter
____ Frequency of a class divided by the sum of all frequencies
____ Measure of how far, on average, the values in a data set are from the mean ____ The test statistic for this procedure follows the F-distribution.
____ Events A and B are ___________________ if P(A and B) = 0.

Location(s) eliminated:

A food fest is organised at the JLN stadium. The stalls from different states and cities have been set up. To make the fest more interesting, multiple games have been arranged which can be played by the people to win the food vouchers. One such game to win the food vouchers is described below:There are N number of boxes arranged in a single queue. Each box has an integer I written on it. From the given queue, the participant has to select two contiguous subsequences A and B of the same size. The selected subsequences should be such that the summation of the product of the boxes should be maximum. The product is not calculated normally though. To make the game interesting, the first box of subsequence A is to be multiplied by the last box of subsequence B. The second box of subsequence A is to be multiplied by the second last box of subsequence B and so on. All the products thus obtained are then added together.


If the participant is able to find the correct such maximum summation, he/she will win the game and will be awarded the food voucher of the same value.


Note: The subsequences A and B should be disjoint.


Example:

Number of boxes, N = 8

The order of the boxes is provided below:





Subsequence A





Subsequence B





The product of the subsequences will be calculated as below:





P1 = 9 * 8 = 72

P2 = 2 * 7 = 14

P3 = 3 * 6 = 18


Summation, S = P1 + P2 + P3 = 72 + 14 + 18 = 104


This is the maximum summation possible as per the requirement for the given N boxes.


Tamanna is also in the fest and wants to play this game. She needs help in winning the game and is asking for your help. Can you help her in winning the food vouchers?



Input Format
The first line of input consists of the number of boxes, N.

The second line of input consists of N space-separated integers.



Constraints
1< N <=3000

-106 <= I <=106

Output Format
Print the maximum summation of the product of the boxes in a separate line.

Sample TestCase 1
Input
8
1 9 2 3 0 6 7 8
Output
104
Explanation
As explained in the example above.

Time Limit(X):
0.50 Sec(S) For Each Input.
Memory Limit:
512 MB
Source Limit:
100 KB

Problem IX A,B,C: Consider the following valuations table for five consumers willing to purchase two differently colored T-shirts:

a) Assuming no production costs, what is the most profitable way to price these two goods independently? What are the prices and resulting profit?

b) Assuming no production costs, what is the most profitable way to price these two goods using bundling? Analyze both pure and mixed bundling, state the prices and resulting profits and choose the best option.

c) Assuming costs of production of $27 per t-shirt (regardless of color), what is the most profitable bundling pricing strategy? Specify whether it’s better to use mixed or pure bundling, then record the optimal prices and resulting profit.

Please answer this question in complete detail as I don't understand this subject too well. Thank you

A scheduled payment of $8,000 due in one year is to be replaced with two payments: the first due in 7 months and the second due in 22 months. Calculate the size of the two payments if the second payment is to be twice as large as the first payment, and money can earn 6% compounded monthly.

The table below shows the hours of relief provided by two analgesic drugs in 12 patients suffering from arthritis. Is there any evidence that one drug provides longer relief than the other? Use Wilcoxon Signed-RankTest.

Case    A         B

1          2.0       3.5

2          14.9     16.7

3          3.6       5.7

4          6.6       6.0

5          2.6       2.9

6          2.3       3.8

7          2.6       2.4

8          2.0       4.0

9          7.3       9.9

10        6.8       9.1

11        3.4       3.3

12        8.5       20.9

A firm is considering replacing the existing industrial air conditioning unit. They will pick one of two units. The first, the AC360, costs $26,454.00 to install, $5,152.00 to operate per year for 7 years at which time it will be sold for $7,182.00. The second, RayCool 8, costs $41,990.00 to install, $2,150.00 to operate per year for 5 years at which time it will be sold for $9,054.00. The firm’s cost of capital is 6.22%. What is the equivalent annual cost of the RayCool8? Assume that there are no taxes.

Can you show me how you solved even if it was done in excel. Thanks!

A firm is considering replacing the existing industrial air conditioning unit. They will pick one of two units. The first, the AC360, costs $26,708.00 to install, $5,045.00 to operate per year for 7 years at which time it will be sold for $7,180.00. The second, RayCool 8, costs $41,711.00 to install, $2,042.00 to operate per year for 5 years at which time it will be sold for $9,069.00. The firm’s cost of capital is 5.34%. What is the equivalent annual cost of the AC360? Assume that there are no taxes.

Can you show me how you solved even if it was done in excel. Thanks!

In the oligopoly sector there are two companies, Enterprise A and Enterprise B, which compete for higher profits. To achieve this, they are considering whether or not to increase their advertising costs. If neither company raises its advertising costs, they split the market and earn € 7 billion each. Should both increase their advertising spending, they will again share the market but make less than € 5 billion each. Moreover, if only one company increased its advertising costs, it would achieve profits of € 8 billion while the other only € 2 billion.

Find the Nash equilibrium with the help of the odds table.

A passcode can have 4 or 5 digits. Digits can be repeated and leading 0s are allowed. So, 1234 would be a 4 digit code that is different from 01234, which is a 5 digit code. How many different passcodes are possible?