int

50+20 * (50/4) /4

. You must use Excel (submit either a pdf, word or Excel file only).

. You must identify the 5 steps (you must address each in detail).

Problem: Use the given data to complete a t-test using Excel.

Question: Is there a difference in group means between the number of words spelled correctly for two groups of fourth graders?

The following frequency table summarizes a set of data. What is the five-number summary?

Select the correct answer below:

Constant Yield Harvesting. In this problem, we assume that fish are caught at a constant rate h independent of the size of the fish population, that is, the harvesting rate H(y, t) = h. Then y satisfies dy/dt = r(1 − y/K )y − h = f (y). (ii) The assumption of a constant catch rate h may be reasonable when y is large but becomes less so when y is small.

(a) If h < rK/4, show that Eq. (ii) has two equilibrium points y1 and y2 with y1 < y2; determine these points.

(b) Show that y1 is unstable and y2 is asymptotically stable.

(c) From a plot of f (y) versus y, show that if the initial population y0 > y1, then y → y2 as t → ∞, but if y0 < y1, then y decreases as t increases. Note that y = 0 is not an equilibrium point, so if y0 < y1, then extinction will be reached in a finite time.

(d) If h > rK/4, show that y decreases to zero as t increases regardless of the value of y0. (e) If h = rK/4, show that there is a single equilibrium point y = K/2 and that this point is semistable. Thus the maximum sustainable yield is hm = rK/4, corresponding to the equilibrium value y=K/2. Observe that hm has the same value as Y m in Problem 1

(d). The fishery is considered to be overexploited if y is reduced to a level below K/2.

(e) If h = rK/4, show that there is a single equilibrium point y = K/2 and that this point is semistable. Thus the maximum sustainable yield is hm = rK/4, corresponding to the equilibrium value y=K/2. Observe that hm has the same value as Y m in Problem 1(d). The fishery is considered to be overexploited if y is reduced to a level below K/2

*Using Matlab

An expert reviews a sample of 10 scientific articles (n = 10) and records the following number of errors in each article: 4, 6, 3, 5, 2, 8, 4, 7, 1, and 4. Compute SS, variance, and standard deviation for this sample using the definitional and computational formula. (Round your answers to two decimal places.)

Consider rolling two dice and let (X, Y) be the random variable pair defined such that X is the sum of the rolls and Y is the maximum of the rolls.

Find the following:

(1) E[X/Y]

(2) P(X > Y )

(3) P(X = 7)

(4) P(Y ≤ 4)

(5) P(X = 7, Y = 4)

1)

What's the result of calling method blitz passing strings "Aquamarine" as the first argument and "Heliotrope" as the second argument?

static int blitz(String v, String w) {
    if (v.length() != w.length())
        return 0;
    int c = 0;
    for (int i = 0; i < v.length(); i++)
        if (v.charAt(i) == w.charAt(i))
            c++;
    return c;
}

a)0

b)1

c)2

d) 3

2)What is NOT an advantage of dynamic arrays compared to static arrays?

a)new elements can be added

b)elements can be inserted

c)elements can be individually indexed

d)elements can be removed

3)

Consider the following code segment:

ArrayList<Integer> scores = new ArrayList<>();

scores.add(5);

scores.add(8);

scores.add(1);

scores.add(1, 9);

scores.remove(2);

scores.add(0, 2);

What's the content of array scores after the code is executed?

a)[2, 5, 8, 1]

b)[2, 5, 9, 1]

c)[5, 2, 9, 1]

d) something else

4)

Consider the following code segment:

int mat[][] = new int[4][3];
for (int i = 0; i < mat.length; i++)
  for (int j = 0; j < mat[0].length; j++)
    if (i % 2 == 0)
      mat[i][j] = 2;
    else if (i % 3 == 0)
      mat[i][j] = 3;
    else
      mat[i][j] = 0;

What is the content of mat's 3rd row after the code segment is executed?

a)[3, 3, 3, 3]

b)[3, 3, 3]

c)[2, 2, 2, 2]

d)[2, 2, 2]

THE MARKET FOR APPLE PIES IN THE CITY ECTENCIA IS COMPETITIVE AND HAS THE FOLLOWING DEMAND SCHEDULE.

EACH PRODUCER IN THE MARKET HAS A FIXED COST OF $9 AND THE FOLLOWING MARGINAL COST.

COMPLETE THE FOLLOWING TABLE BY COMPUTING THE TOTAL COST AND AVERAGE TOTAL COST FOR EACH QUANITY PRODUCED.

THE PRICE OF THE PIE IS NOW $11

AT A PRICE OF $11, ___??? PIES ARE SOLD IN THE MARKET. EACH PRODUCER MAKES___ ???PIES. SO THERE ARE ____?? PRODUCERS IN THIS MARKET, EACH MAKING A PROFIT OF $____???

TRUE OR FALSE: THE MARKET IS IN LONG RUN EQUILIBRIUM

SUPPOSE IN THE LONG RUN THERE IS FREE ENTRY AND EXIT.

IN THE LONG RUN, EACH PRODUCER EARNS A PROFIT OF $_____???. THE MARKET PRICE IS $____???. AT THIS PRICE, ___??? PIES ARE SOLD IN THIS MARKET, AND EACH PRODUCER MAKES ___??? PIES, SO THERE ARE ____??? PRODUCERS OPERATING.

Fourier Series Approximation Matlab HW1:
   

You are given a finite step function  
x(t)=-1, 0<t<4
         1, 4<t<8 .

Hand calculate the FS coefficients of x(t) by assuming half- range expansion,  for each case below and modify the code.

Approximate x(t) by cosine series only (This is even-half range expansion). Modify the below code and plot the approximation showing its steps changing by included number of FS terms in the approximation.

Approximate x(t) by sine series only (This is odd-half range expansion).. Modify the below code and plot the approximation showing its steps changing by included number of FS terms in the approximation.

You are given a code below which belongs to a different function, if you run this code it works and you will see it belongs to ft=1 0<t<2 0 2<t<4 . In this code f(t) is only approximated by even coefficients (cosine series).
Upload to BB learn using the Matlab HW1 link:
A multi page pdf file that shows

The hand calculations of FS coefficients

The original function plotted

The approximated functions plotted for b and c.

A Comment on how FS expansion approximates discontinuities in the function.

MATLAB CODE
_____________________________________________________________________________________________________________________________________________________________________
clear all
close all
% Example MATLAB M-file that plots a Fourier series
% Set up some input values
P = 4; %period = 2P
num_terms = 100; %approximate infinite series with finite number of terms
% Miscellaneous setup stuff
format compact;  % Gets rid of extra lines in output. Optional.
% Initialize x-axis values from -1.25L to 1.25L. Middle number is step size. Make
% middle number smaller for smoother plots
t = -4:0.001:4;
x=zeros(length(t),1);   % reseting original half range expanded function array
x(0<=t & t<2)=1;       % forming the original half range expanded function array for the purpose of plotting only
x(2<t & t <4)=0;
x(t<0 & -2<t)=1;
x(t<-2 & t>-4)=0;
figure     %plotting original half range expanded function
plot(t,x)
axis([-4.5 4.5 -0.5 1.5])
%Starting to approximate f(t)
% Initialize y-axis values.  y = f(t)
f = zeros(size(x'));
% Add a0/2 to series
a0 = 1;
f = f + a0/2;
% Loop num_terms times through Fourier series, accumulating in f.
figure
for n = 1:num_terms
   
 
   
   % Formula for an.
   an = (2/(n*pi))*sin(n*pi/2);
       bn=0;
   
   % Add cosine and sine into f
   f = f + an*cos(n*pi*t/P) + bn*sin(n*pi*t/P);
   
   % Plot intermediate f.  You can comment these three lines out for faster
   % execution speed.  The function pause(n) will pause for about n
   % seconds.  You can raise or lower for faster plots.
   plot(t,f);
   set(gca,'FontSize',16);
   title(['Number of terms = ',num2str(n)]);
   grid on;
   if n < 5
       pause(0.15);
   else
       pause(0.1);
   end
   xlabel('even approx');
end;

1. Anderson Manufacturing orders four types of components for their new wireless headset from two suppliers. The number of units received from a recent order is summarized in the table below:

1. What proportion of the units were received from supplier 2? (1 mark)
2. What proportion of the components received were Component 2? (1 mark)
3. What proportion of Component 2 units received were from Supplier 1? (1 mark)
4. What proportion of the units received from Supplier 2 were Component 3? (1 mark)