A SI bet in a state lottery's Pick 3 game pays $500 if the three-digit number you choo se exactlymatches the winning number, which is drawn at random. Here is the distribution of the payoff X:1.Payoff XProbability$5000.9990.001Each day's drawing is independent of other drawings. You must show your work in answeringthe following questionsWhat are the mean and standard deviation of X?a.b. Joe buys a Pick 3 ticket twice a week. What does the law of large numbers say about the averagepayoff Joe receives from his bets?c. What does the central limit the orem say about the distribution of Joe's average payoff after 104bets in a year?d.Joe comes out ahead for the year if his average payoff is greater than $1(the amount he spent eachday on a ticket). What is the probability that Joe ends the year he ad?

Question
Asked Oct 19, 2019
A SI bet in a state lottery's Pick 3 game pays $500 if the three-digit number you choo se exactly
matches the winning number, which is drawn at random. Here is the distribution of the payoff X:
1.
Payoff X
Probability
$500
0.999
0.001
Each day's drawing is independent of other drawings. You must show your work in answering
the following questions
What are the mean and standard deviation of X?
a.
b. Joe buys a Pick 3 ticket twice a week. What does the law of large numbers say about the average
payoff Joe receives from his bets?
c. What does the central limit the orem say about the distribution of Joe's average payoff after 104
bets in a year?
d.
Joe comes out ahead for the year if his average payoff is greater than $1(the amount he spent each
day on a ticket). What is the probability that Joe ends the year he ad?
help_outline

Image Transcriptionclose

A SI bet in a state lottery's Pick 3 game pays $500 if the three-digit number you choo se exactly matches the winning number, which is drawn at random. Here is the distribution of the payoff X: 1. Payoff X Probability $500 0.999 0.001 Each day's drawing is independent of other drawings. You must show your work in answering the following questions What are the mean and standard deviation of X? a. b. Joe buys a Pick 3 ticket twice a week. What does the law of large numbers say about the average payoff Joe receives from his bets? c. What does the central limit the orem say about the distribution of Joe's average payoff after 104 bets in a year? d. Joe comes out ahead for the year if his average payoff is greater than $1(the amount he spent each day on a ticket). What is the probability that Joe ends the year he ad?

fullscreen
check_circle

Expert Answer

Step 1

Hey, since there are multiple subparts posted, we will answer first three subparts. If you want any specific subpart to be answered, then please submit that subpart only or specify the subpart number in your message.

Step 2

a).

The expected value (mean) can be obtained as follows:

E(X)-ΣχxP()
(0x0.999)+(500x 0.001)
=0.5
help_outline

Image Transcriptionclose

E(X)-ΣχxP() (0x0.999)+(500x 0.001) =0.5

fullscreen
Step 3

Now, calculate E(x2) as g...

E(X) - Σέx P(3)
(03x 0.999)+(5002 x 0.001)
=250
help_outline

Image Transcriptionclose

E(X) - Σέx P(3) (03x 0.999)+(5002 x 0.001) =250

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Statistics

Advanced Topics in Statistics

Related Statistics Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: A researcher measured BMI in 12 patients who are free of diabetes and participating in a study of ri...

A: Confidence interval when population standard deviation is not known:The formula of confidence interv...

question_answer

Q: A test of hypothesis is statistic  H0: u=150 versus H1:u greater than 150 was performed. The P-value...

A: From the provided information considering u=150, the test hypothesis is provided as:

question_answer

Q: The General Social Survey asks questions about one’s happiness in marriage. Is there an association ...

A: (a)The frequency marginal distribution is,

question_answer

Q: If the mean height of a population of university students is 166cm (μ=166) and the standard deviatio...

A: Consider,X be the height of students which follows normal distribution with mean of 166 cm and stand...

question_answer

Q: Each car in a sample of seven cars was tested for nitrogen-oxide emissions (in grams per mile), and ...

A: Enter the data in excel as shown below and the following formula to get the mean, standard deviation...

question_answer

Q: x bar is an estimate of?

A: Population:The set of all subjects of interest can be termed as population.Sample:The subset of the ...

question_answer

Q: E and F are mutually exclusive events. P(E) = 0.1; P(F) = 0.6. Find P(E | F)

A: From the given information, P(E)=0.1 and P(F)=0.6.The events E and F are mutually exclusive events. ...

question_answer

Q: In a certain shipment of 19 computers, 11 are defective. 7 of the computers are selected at random w...

A: Given dataTotal computers = 19No of defectives = 11

question_answer

Q: In the 1992 presidential election, Alaska's 40 election districts averaged 1898 votes per district f...

A: Given: