expected - results or observations that are predicted

2 Asset Portfolio

Given a portfolio with 2 assets, this determines the expected return (mean), variance, and volatility (standard deviation) of the portfolio.

3 boys share 100 in the ratio 1:2:2. how much each boy will get?

3 boys share 100 in the ratio 1:2:2. how much each boy will get?
Given the ratio 1 : 2 : 2, calculate the expected number of items from a population of 100
A ratio of 1 : 2 : 2 means that for every of item A, we can expect 2 of item B and 2 of item c
Therefore, our total group is 1 + 2 + 2 = 5
[SIZE=5][B]Calculate Expected Number of Item A:[/B][/SIZE]
Expected Number of Item A = 1 x 100/5
Expected Number of Item A = 100/5
Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=100&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5
Expected Number of Item A = 20/1
Expected Number of Item A = [B]20[/B]
[SIZE=5][B]Calculate Expected Number of Item B:[/B][/SIZE]
Expected Number of Item B = 2 x 100/5
Expected Number of Item B = 200/5
Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=200&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5
Expected Number of Item B = 40/1
Expected Number of Item B = [B]40[/B]
[SIZE=5][B]Calculate Expected Number of Item C:[/B][/SIZE]
Expected Number of Item C = 2 x 100/5
Expected Number of Item C = 200/5
Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=200&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5
Expected Number of Item C = 40/1
Expected Number of Item C = [B]40[/B]
[B]Final Answer:[/B]
(A, B, C) =[B] (20, 40, 40)[/B] for 1:2:2 on 100 people

A basket of goods was valued at $45.40 in January 2011. The inflation rate for the year was 4%. What

A basket of goods was valued at $45.40 in January 2011. The inflation rate for the year was 4%. What is the expected cost of the basket of goods in January 2012? Write your answer to the nearest cent.
2012 cost = 2011 cost * (1 + I/100)
2012 cost = 45.40 * (1 + 4/100)
2012 cost = 45.40 * (1 + 0.04)
2012 cost = 45.40 * (1.04)
2012 cost = [B]47.22[/B]

A bowler knocks down at least 6 pins 70 percent of the time. Out of 200 rolls, how many times can yo

A bowler knocks down at least 6 pins 70 percent of the time. Out of 200 rolls, how many times can you predict the bowler will knock down at least 6 pins?
Expected Value of (knocking down at least 6 pins) = number of rolls * probability of knocking down at least 6 pins
Expected Value of (knocking down at least 6 pins) = 200 * 0.7
Expected Value of (knocking down at least 6 pins) = [B]140[/B]

a cash prize of $4600 is to be awarded at a fundraiser. if 2300 tickets are sold at $7 each, find th

a cash prize of $4600 is to be awarded at a fundraiser. if 2300 tickets are sold at $7 each, find the expected value.
Expected Value E(x) is:
E(x) = Probability of winning * Winning Price - Probability of losing * Ticket Price
[U]Since only 1 cash price will be given, 2299 will be losers:[/U]
E(x) = 4600 * (1/2300) - 2299/2300 * 7
E(x) = 2 - 0.99956521739 * 7
E(x) - 2 - 7
E(x) = [B]-5[/B]

A chicken farm produces ideally 700,000 eggs per day. But this total can vary by as many as 60,000 e

A chicken farm produces ideally 700,000 eggs per day. But this total can vary by as many as 60,000 eggs. What is the maximum and minimum expected production at the farm?
[U]Calculate the maximum expected production:[/U]
Maximum expected production = Average + variance
Maximum expected production = 700,000 + 60,000
Maximum expected production = [B]760,000[/B]
[U]Calculate the minimum expected production:[/U]
Minimum expected production = Average - variance
Minimum expected production = 700,000 - 60,000
Minimum expected production = [B]640,000[/B]

A coffee franchise is opening a new store. The company estimates that there is a 75% chance the sto

A coffee franchise is opening a new store. The company estimates that there is a 75% chance the store will have a profit of $45,000, a 10% chance the store will break even, and a 15% chance the store will lose $2,500. Determine the expected gain or loss for this store.
Calculate the expected value E(x). Expected value is the sum of each event probability times the payoff or loss:
E(x) = 0.75(45,000) + 0.1(0) + 0.15(-2,500) <-- Note, break even means no profit and no loss and a loss is denoted with a negative sign
E(x) = 33,750 + 0 - 375
E(x) = [B]33,375 gain[/B]

A company has 3,100 employees and is expected to grow at a rate of 0.04 for the next six years. How

A company has 3,100 employees and is expected to grow at a rate of 0.04 for the next six years. How many employees will they have in 6 years? Round to the nearest whole number.
We build the following exponential equation:
Final Balance = Initial Balance * (1 + growth rate)^time
Final Balance = 3100(1.04)^6
Final Balance = 3100 * 1.2653190185
Final Balance = 3922.48895734
The problem asks us to round to the nearest whole number. Since 0.488 is less than 0.5, we round [U]down.[/U]
Final Balance = [B]3,922[/B]

A lottery offers 1 $1000 prize and 5 $100 prizes. 1000 tickets are sold. Find the expectation if a p

A lottery offers 1 $1000 prize and 5 $100 prizes. 1000 tickets are sold. Find the expectation if a person buys 1 ticket for $5.
Set up the expected values E(x):
for the 1,000 price:
E(x) = (1000 - 5) * 1/1000 = 995/1000
For the 5 $100 prizes:
E(x) = (100 - 5) * 5/1000 = 475/1000
For the losing ticket. With 6 winning tickets, we have 1000 - 6 = 994 losing tickets:
E(x) = -3 * 994/1000 = -2982/1000
We get our total expected value by adding all of these expected values up. Since they all have the same denominator, we add numerators:
E(x) = (995 + 475 - 2982)/1000
E(x) = -1512/1000
E(x) = [B]-1.51[/B]

A private high school charges $36,400 for tuition, but this figure is expected to rise 10% per year.

A private high school charges $36,400 for tuition, but this figure is expected to rise 10% per year. What will tuition be in 10 years?
Let the tuition be T(y) where y is the number of years from now. We've got:
T(y) = 36400 * (1.1)^y
The problem asks for T(10)
T(10) = 36400 * (1.1)^10
T(10) = 36400 * 2.5937424601
T(10) = [B]94,412.23[/B]

A private high school charges $52,200 for tuition, but this figure is expected to rise 7% per year.

A private high school charges $52,200 for tuition, but this figure is expected to rise 7% per year. What will tuition be in 3 years?
We have the following appreciation equation A(y) where y is the number of years:
A(y) = Initial Balance * (1 + appreciation percentage)^ years
Appreciation percentage of 7% is written as 0.07, so we have:
A(3) = 52,200 * (1 + 0.07)^3
A(3) = 52,200 * (1.07)^3
A(3) = 52,200 * 1.225043
A(3) = [B]63,947.25[/B]

A spinner is divided into 4 equal sections numbered 1 to 4. The theoretical probability of the spinn

A spinner is divided into 4 equal sections numbered 1 to 4. The theoretical probability of the spinner stopping on 3 is 25%. Which of the following is most likely the number of 3s spun in 10,000 spins?
We want Expected Value of s spins. Set up the expected value formula for any number 1-4
E(s) = 0.25 * n where n is the number of spins.
Using s = 3, n = 10,000, we have:
E(10,000) = 0.25 * 10,000
E(10,000) = [B]2,500[/B]

An organic juice bottler ideally produces 215,000 bottle per day. But this total can vary by as much

An organic juice bottler ideally produces 215,000 bottle per day. But this total can vary by as much as 7,500 bottles. What is the maximum and minimum expected production at the bottling company?
Our production amount p is found by adding and subtracting our variance amount:
215,000 - 7,500 <= p <= 215,000 + 7,500
[B](min) 207,500 <= p <=222,500 (max)[/B]

Assume the speed of vehicles along a stretch of I-10 has an approximately normal distribution with a

Assume the speed of vehicles along a stretch of I-10 has an approximately normal distribution with a mean of 71 mph and a standard deviation of 8 mph.
a. The current speed limit is 65 mph. What is the proportion of vehicles less than or equal to the speed limit?
b. What proportion of the vehicles would be going less than 50 mph?
c. A new speed limit will be initiated such that approximately 10% of vehicles will be over the speed limit. What is the new speed limit based on this criterion?
d. In what way do you think the actual distribution of speeds differs from a normal distribution?
a. Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=65&mean=71&stdev=8&n=+1&pl=P%28X+%3C+Z%29']z-score calculator[/URL], we see that P(x<65) = [B]22.66%[/B]
b. Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+50&mean=71&stdev=8&n=+1&pl=P%28X+%3C+Z%29']z-score calculator[/URL], we see that P(x<50) = [B]0.4269%[/B]
c. [URL='http://www.mathcelebrity.com/zcritical.php?a=0.9&pl=Calculate+Critical+Z+Value']Inverse of normal for 90% percentile[/URL] = 1.281551566
Plug into z-score formula: (x - 71)/8 = 1.281551566
[B]x = 81.25241252[/B]
d. [B]The shape/ trail differ because the normal distribution is symmetric with relatively more values at the center. Where the actual has a flatter trail and could be expected to occur.[/B]

Basic Statistics

Given a number set, and an optional probability set, this calculates the following statistical items:

Expected Value

Mean = μ

Variance = σ^{2}

Standard Deviation = σ

Standard Error of the Mean

Skewness

Mid-Range

Average Deviation (Mean Absolute Deviation)

Median

Mode

Range

Pearsons Skewness Coefficients

Entropy

Upper Quartile (hinge) (75th Percentile)

Lower Quartile (hinge) (25th Percentile)

InnerQuartile Range

Inner Fences (Lower Inner Fence and Upper Inner Fence)

Outer Fences (Lower Outer Fence and Upper Outer Fence)

Suspect Outliers

Highly Suspect Outliers

Stem and Leaf Plot

Ranked Data Set

Central Tendency Items such as Harmonic Mean and Geometric Mean and Mid-Range

Root Mean Square

Weighted Average (Weighted Mean)

Frequency Distribution

Successive Ratio

Expected Value

Mean = μ

Variance = σ

Standard Deviation = σ

Standard Error of the Mean

Skewness

Mid-Range

Average Deviation (Mean Absolute Deviation)

Median

Mode

Range

Pearsons Skewness Coefficients

Entropy

Upper Quartile (hinge) (75th Percentile)

Lower Quartile (hinge) (25th Percentile)

InnerQuartile Range

Inner Fences (Lower Inner Fence and Upper Inner Fence)

Outer Fences (Lower Outer Fence and Upper Outer Fence)

Suspect Outliers

Highly Suspect Outliers

Stem and Leaf Plot

Ranked Data Set

Central Tendency Items such as Harmonic Mean and Geometric Mean and Mid-Range

Root Mean Square

Weighted Average (Weighted Mean)

Frequency Distribution

Successive Ratio

Chuck-a-luck is an old game, played mostly in carnivals and county fairs. To play chuck-a-luck you p

Chuck-a-luck is an old game, played mostly in carnivals and county fairs. To play chuck-a-luck you place a bet, say $1, on one of the numbers 1 through 6. Say that you bet on the number 4. You then roll three dice (presumably honest). If you roll three 4’s, you win $3.00; If you roll just two 4’s, you win $2; if you roll just one 4, you win $1 (and, in all of these cases you get your original $1 back). If you roll no 4’s, you lose your $1. Compute the expected payoff for chuck-a-luck.
Expected payoff for each event = Event Probability * Event Payoff
Expected payoff for 3 matches:
3(1/6 * 1/6 * 1/6) = 3/216 = 1/72
Expected payoff for 2 matches:
2(1/6 * 1/6 * 5/6) = 10/216 = 5/108
Expected payoff for 1 match:
1(1/6 * 5/6 * 5/6) = 25/216
Expected payoff for 0 matches:
-1(5/6 * 5/6 * 5/6) = 125/216
Add all these up:
(3 + 10 + 25 - 125)/216
-87/216 ~ [B]-0.40[/B]

Equivalent Annual Cost (EAC)

Given 2 Items/machines with an Investment Cost, expected lifetime, and maintenance cost, this will calculate the EAC for each Item/machine as well as draw a conclusion on which project to invest in.

Expected Frequency

Given a contingency table (two-way table), this will calculate expected frequencies and then determine a conclusion based on a Χ^{2} test with critical value test and conclusion.

Expected Value

This lesson walks you through what expected value is, expected value notation, the expected value of a discrete random variable, the expected value of a continuous random variable, and expected value properties.

Finance

1. Spend 8000 on a new machine. You think it will provide after tax cash inflows of 3500 per year for the next three years. The cost of funds is 8%. Find the NPV, IRR, and MIRR. Should you buy it?
2. Let the machine in number one be Machine A. An alternative is Machine B. It costs 8000 and will provide after tax cash inflows of 5000 per year for 2 years. It has the same risk as A. Should you buy A or B?
3. Spend 100000 on Machine C. You will need 5000 more in net working capital. C is three year MACRS. The cost of funds is 8% and the tax rate is 40%. C is expected to increase revenues by 45000 and costs by 7000 for each of the next three years. You think you can sell C for 10000 at the end of the three year period.
a. Find the year zero cash flow.
b. Find the depreciation for each year on the machine.
c. Find the depreciation tax shield for the three operating years.
d. What is the projects contribution to operations each year, ignoring depreciation effects?
e. What is the cash flow effect of selling the machine?
f. Find the total CF for each year.
g. Should you buy it?

Given that E[Y]=2 and Var [Y] =3, find E[(2Y + 1)^2]

Given that E[Y]=2 and Var [Y] =3, find E[(2Y + 1)^2]
Multiply through
E[(2Y + 1)^2] = E[4y^2 + 4y + 1]
We can take the expected value of each term
E[4y^2] + E[4y] + E[1]
For the first term, we have:
4E[Y^2]
We define the Var[Y] = E[Y^2] - (E[Y])^2
Rearrange this term, we have E[Y^2] = Var[Y] + (E[Y])^2
E[Y^2] = 3+ 2^2
E[Y^2] = 3+ 4
E[Y^2] = 7
So our first term is 4(7) = 28
For the second term using expected value rules of separating out a constant, we have
4E[Y] = 4(2) = 8
For the third term, we have:
E[1] = 1
Adding up our three terms, we have:
E[4y^2] + E[4y] + E[1] = 28 + 8 + 1
E[4y^2] + E[4y] + E[1] = [B]37[/B]

In 2016 the geese population was at 750. the geese population is expected to grow at a rate of 12% e

In 2016 the geese population was at 750. the geese population is expected to grow at a rate of 12% each year. What is the geese population in 2022?
12% is also 0.12. We have the population growth function:
P(t) = 750(1.12)^t
2022 - 2016 is 6 years of growth. We want P(6).
P(6) = 750(1.12)^6
P(6) = 750(1.9738)
[B]P(6) = 1,480.36 ~ 1,480[/B]

Jerry rolls a dice 300 times what is the estimated numbers the dice rolls on 6

Jerry rolls a dice 300 times what is the estimated numbers the dice rolls on 6
Expected Value = Rolls * Probability
Since a 6 has a probability of 1/6, we have:
Expected Value = 300 * 1/6
Expected Value = [B]50[/B]

Prizes hidden on a game board with 10 spaces. One prize is worth $100, another is worth $50, and tw

Imagine you are in a game show. Prizes hidden on a game board with 10 spaces. One prize is worth $100, another is worth $50, and two are worth $10. You have to pay $20 to the host if your choice is not correct. Let the random variable x be the winning
(a) What is your expected winning in this game?
(b) Determine the standard deviation of x. (Round the answer to two decimal places)
(a) 100(0.1) + 50(0.1) + 10(0.2) - 20 = 10 + 5 + 2 - 20 = [B]-3[/B]
(b) 3.3 using our [URL='http://www.mathcelebrity.com/statbasic.php?num1=+100,50,10&num2=+0.1,0.1,0.2&usep=usep&pl=Number+Set+Basics']standard deviation calculator[/URL]

Ratios

* Simplifies a ratio of a:b

* Given a ratio in the form a:b or a to b, and a total population amount, this calculator will determine the expected value of A and B from the ratio.

* Given a ratio in the form a:b or a to b, and a total population amount, this calculator will determine the expected value of A and B from the ratio.

Roulette

Calculates the probability for different bets on a roulette wheel including expected return on a monetary bet.

Security Market Line and Treynor Ratio

Solves for any of the 4 items in the Security Market Line equation, Risk free rate, market return, Β, and expected return as well as calculate the Treynor Ratio.

Suppose a computer chip manufacturer knows from experience that in an average production run of 5000

Suppose a computer chip manufacturer knows from experience that in an average production run of 5000 circuit boards, 100 will be defective. How many defective circuit boards can be expected in a run of 24,000 circuit boards?
100 defective / 5000 circuit boards * 24,000 circuit boards = [B]480 defective circuit boards[/B]

The chance of a soldier being an enemy spy is .0005. Out of 10,000 soldiers, how many of them are ex

The chance of a soldier being an enemy spy is .0005. Out of 10,000 soldiers, how many of them are expected to be spies?
Expected Spies = Probability of being a spy * Total Soldiers
Expected Spies = 0.0005 * 10000
Expected Spies = [B]5[/B]

The temperature in Chicago was five (5) degrees Celsius in the morning and is expected to drop by as

The temperature in Chicago was five (5) degrees Celsius in the morning and is expected to drop by as much as 12 degrees during the day. What is the lowest temperature in Chicago for the day?
We start with 5 celsius
A drop in temperature means we subtract
5 - 12 = [B]-7 or 7 degrees below zero[/B]

Today a car is valued at $42000. the value is expected to decrease at a rate of 8% each year. what i

Today a car is valued at $42000. the value is expected to decrease at a rate of 8% each year. what is the value of the car expected to be 6 years from now.
Depreciation at 8% per year means it retains (100% - 8%) = 92% of it's value. We set up our depreciation function D(t), where t is the number of years from right now.
D(t) = $42,000(0.92)^t
The problem asks for D(6):
D(6) = $42,000(0.92)^6
D(6) = $42,000(0.606355)
D(6) = [B]$25,466.91[/B]

Volatility

Given a set of stock prices, this determines expected rates of return and volatility