The accompanying data set provides the closing prices for four stocks and the stock exchange over 12 days:

With the help of the Excel Exponential Smoothing tool, I was able to forecast each of the stock prices using simple exponential smoothing with a smoothing constant of 0.3 (ie, damping factor of 0.7). I was also able to calculate the MAD of each of the stocks:

MAD of Stock A = 1.32

MAD of Stock B = 0.37

MAD of Stock C = 0.41

MAD of Stock D = 0.26

MAD of Stock Exchange = 83.85

Help me to calculate the Mean Square Error (MSE) of the stocks.

2. A fire detector uses 3 sensors with a sensitivity level of 0.8 each (meaning the probability that a sensor will turn on if the room temperature reaches 100oC or more is 0.8). A fire alarm will sound if at least one sensor is on. Suppose Y is a random variable that states the number of sensors that are on, then specify:

a. Possible values for Y!

b. Probability function for random variable Y1

c. Y score and variance.

d. What are the probability of the device providing incorrect information?

Let X have a binomial distribution with parameters

n = 25

and p. Calculate each of the following probabilities using the normal approximation (with the continuity correction) for the cases

p = 0.5, 0.6, and 0.8

and compare to the exact binomial probabilities calculated directly from the formula for

b(x; n, p).

(Round your answers to four decimal places.)

P(20 ≤ X)

Using Runge-Kutta method of order 4 to approximate y(1) with step size h = 0.1 and h = 0.2 respectively (keep 8 decimals):

dy/dx = x + arctan y, y(0) = 0.

Solutions: when h = 0.1, y(1) = 0.70398191. when h = 0.2, y(1) = 0.70394257.

Given the following excess rainfall hyetograph and 1-hr unit hydrograph, what would the 5th ordinate of the storm hydrograph be in cfs? Pn (intervals of 1 hr) = [0.2, 0.4 ,0.5 ,0.2 ,0 ,0.1] in UH (intervals of 1 hr) = [0, 100, 320, 450, 370, 250, 160, 90, 40, 0] cfs

Change in concentration of salt in a reactor can be modeled
by the following equation y’ = ty+y1/2
Initial concentration of salt at time (t= 0 hours) is 1g/l, y(0)=
1, find the concentration of salt after 0.2 hour y(0.2)= ? by
using Euler, Heun and RK4 methods. Use h= 0.1

The Butler-Perkins Company (BPC) must decide between two mutually exclusive projects. Each project has an initial outflow of $6,750 and has an expected life of 3 years. Annual project cash flows begin 1 year after the initial investment and are subject to the following probability distributions:

BPC has decided to evaluate the riskier project at 12% and the less-risky project at 8%.

1. What is each project's expected annual cash flow? Round your answers to the nearest cent.

   Project A:	$
   Project B:	$

   
   Project B's standard deviation (σ_B) is $5,444 and its coefficient of variation (CV_B) is 0.73. What are the values of (σ_A) and (CV_A)? Do not round intermediate calculations. Round your answer for standard deviation to the nearest cent and for coefficient of variation to two decimal places.

   σA:	$
   CVA:

The Butler-Perkins Company (BPC) must decide between two mutually exclusive projects. Each project has an initial outflow of $6,500 and has an expected life of 3 years. Annual project cash flows begin 1 year after the initial investment and are subject to the following probability distributions:

BPC has decided to evaluate the riskier project at 12% and the less-risky project at 10%.

1. What is each project's expected annual cash flow? Round your answers to the nearest cent.

   Project A:	$
   Project B:	$

   
   Project B's standard deviation (σ_B) is $6,185 and its coefficient of variation (CV_B) is 0.80. What are the values of (σ_A) and (CV_A)? Do not round intermediate calculations. Round your answer for standard deviation to the nearest cent and for coefficient of variation to two decimal places.

   σA:	$
   CVA:

The Butler-Perkins Company (BPC) must decide between two mutually exclusive projects. Each project has an initial outflow of $6,750 and has an expected life of 3 years. Annual project cash flows begin 1 year after the initial investment and are subject to the following probability distributions:

BPC has decided to evaluate the riskier project at 11% and the less-risky project at 10%.

1. What is each project's expected annual cash flow? Round your answers to the nearest cent.

   Project A:	$
   Project B:	$

   
   Project B's standard deviation (σ_B) is $5,798 and its coefficient of variation (CV_B) is 0.76. What are the values of (σ_A) and (CV_A)? Do not round intermediate calculations. Round your answer for standard deviation to the nearest cent and for coefficient of variation to two decimal places.

   σA:	$
   CVA:

1. Write the half reactions that occur at the anode and cathode in these electrochemical cells. Annotate which half reaction occurs at the anode and the cathode.

2. Write the overall balance reaction for the following electrochemical cells.

Ag(s), Ag(NO3)2 (1.0 M) || Cu (s), CuCl2 (1.0M)

Zn(s), Zn(NO3)2 (1.0M) || Ni (s), Ni(NO3)2 (1.0M)

Zn(s), Zn(NO3)2 (0.3 M) || Cu(s), CuCl2 (0.5M)

Ag(s), Ag(NO3)2 (0.3 M) || Cu(s), CuCl2 (0.5 M)

Ag(s), Ag(NO3)2 (0.3 M) || Ni(s), Ni(NO3)2 (0.5 M)

Cu(s), CuCl2 (.001 M) || Cu(s), CuCl2 (1.0 M)

Thank you!!!