Random Variable - Mrs. Cohen's Math Classes

Section 5.1.notebook

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November 03, 2014

Feb 29:19 AM

Random VariableNumerical value which depends on chance.

Discrete - countable"count" number of students who . . .number of participants who . . .number of eggs in each nest . . .

Continuous - countless"measure"Things like distance, time, weight . . .

Feb 29:32 AM

Cars Number RelativeOwned of families frequencyx f0 17 0.004251 877 0.219252 1767 0.441753 1107 0.276754 200 0.050005 32 0.00800

4000 1

Can be called relative frequency Or probability distribution.Notice it is discrete because you own 0, 1, 2 cars . . . not 1.34 cars.Discuss how did they get the numbers in the last column.Important that the total at the bottom is 1.


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November 03, 2014

Feb 210:12 AM

These formulas are used for discrete. We will do in our calculator

σ =√Σ(x μ)2P(x)

Feb 210:22 AM

What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Thanks to Florence Nightingale and the British census of 1851, we have the following information.

NOTE:In 1851 there were 25,466 nurses in Great Britain.

Age Midpoint PercentRange(yr) x of Nurses20-29 24.5 5.7%30-39 34.5 9.7%40-49 44.5 19.7%50-59 54.5 29.2%60-69 64.5 25.0%70-79 74.5 9.1%80+ 84.5 1.8%

a) Using the age midpoints x and the percents of nurses, do we have a valid probability distribution? Add up to see if it makes 100%Are the events distinct? does each nurse have one and only one age?


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November 03, 2014

Feb 210:22 AM

b) Use a histogram to graph the probability distribution of part a.

10%

20%

30%

24.5 34.5 44.5 54.5 64.5 74.5 84.5


Feb 210:59 AM

c) Find the probability that a British nurse selected at random in 1851 would be 60 years of age or older. P (60-69 or 70-79 or 80+) Add up the percents/probabilities for 60-69, 70-79 and 80+



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November 03, 2014

Feb 211:07 AM

d) Compute the expected age µ and the standard deviation σ of a British nurse in 1851.enter x values in L1 and percents in L2 do Stat - Calc - 1 VarStats- L1, L2 enter


Feb 211:20 AM

x 0 1 2 3 4 5P(x) 0.237 0.396 0.264 0.088 0.015 0.001a) Find the probability that one or more of the five students will drop outAdd up the probabilities for P(1)+P(2)+P(3)+P(4)+P(5)

OR do 1 - P(0)

b) Find the probability that two or more of the five students will drop out before getting their degree.Add up the probabilities for P(2)+P(3)+P(4)+P(5)

OR do 1 - [P(0) + P(1)]

After long term studies Mrs.Cohen's data showed that 25% of her statistics students that enter college will drop out before getting their degree. Let x = number of statistic students out of 5 who drop out of college.


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November 03, 2014

Feb 211:42 AM

b) Compute μ the expected number of drop outs out of five and σ, the standard deviation for the expected number of drop outs out of five.

x 0 1 2 3 4 5P(x) 0.237 0.396 0.264 0.088 0.015 0.001

Jan 287:48 AM

Bear Creek is having a raffle for a free I phone. Each raffle ticket cost $1.The phone is valued at $280 and was donated to the school. We sold 1200 tickets.

a) you bought 20 tickets. What is the probability that you will win the I phone? What is the probability that you will not win the I phone?

b) Your expected earnings can be found by multiplying the value of the I phone times the probability that you will win the I phone. Find your expected earnings.

c) Your expected contribution = amount of money you spent - your expected earnings.


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November 03, 2014

Jan 287:38 AM

12.

Jan 287:38 AM

13.


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November 03, 2014

Nov 38:25 PM

14. Students do this one. And check their answers.

Assignment: p. 226 #1, 4-6, 10,11,14.

Nov 38:25 PM

Newspaper Route

Joseph was collecting from his customers on his newspaper rout. One of his customers offered him a deal. The customer would place three 1dollar bills, one 5dollar bill and one 10dollar bill in a bag (of course Joseph could not see inside the bag). Joseph would reach in and take one bill from the bag and get paid that instead of his regular $5. Should he take the deal? Or should he insist instead on getting his regular $5? Explain your thinking.


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November 03, 2014

Nov 38:26 PM

Step 3: Find the expected value (AKA the expected earnings)

Step 2: create a relative frequency table of each possible outcome

Step 1: List the sample space

Nov 38:26 PM

GAME 1: Rolling for Dollars!

Charge: $1 per roll

If you roll

6: You get $5

5: You get $2

4: You get $1

3, 2, or 1: You get nothing.


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November 03, 2014

Nov 38:26 PM

GAME 2: Big Bucks!

Charge: $1 to toss 3 coins

Toss the coins.

If you get all heads or all tails, you receive $5.

If not, you get nothing.

Nov 38:26 PM

GAME 3: Toss Away!

Charge: $1

Roll 2 dice.

If you roll 2 odd numbers, like a 3 and a 5, you get $2.

If you roll 2 even numbers, like 4 and 6, you get $2.

Otherwise, you get nothing.


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November 03, 2014

Nov 38:26 PM

GAME 4: Draw a Fortune!

Charge: $5

Draw twice from a bag that has one $10 and 4 $1 bills.

You get to keep the bills.

Nov 38:27 PM

Now it's your turn! Create your own game with the following constraints:

1) The game can have any structure of the previous 4 games2) The game must have clear rules3) The game must have an expected value such that the school makes between 1-50 cents per game.4) Write the rules of the game on one side of you file folder5) Write the sample space of your game, make a histogram that shows the relative frequency, and compute the expected value of the game with all work shown on the back of the file folder.

*HINT* you get to charge what you want. It does not have to be $1 or $5

Random Variable - Mrs. Cohen's Math Classes

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