expected value - predicted value of a variable or event

Formula: E(X) = Σx_{I}· P(x)

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 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 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 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]

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

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.

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]

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]

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.

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]