Please write down all formulas needed to solve and explanation of each formula for Probability, Discrete random variables and their distribution, and continuous distribution. ie from permutation and combination to bayes theorem to binomial. reference to probabilty and statistics for computer scientists 2nd edition.
thanks

Identify the independent variable, the dependent variable, and the unit of analysis in the following hypothesis:

a.       Interstate migration in the United States lowers state poverty levels.

b.      Documented immigrants in the United States are less likely than undocumented immigrants to use social welfare programs.

c.       On average, the annual household income of female-headed households is about 25% less than the annual household income of married couple households.

d.      Geographically, contiguous countries should experience higher rates of migration than noncontiguous countries.

e.       In the United States, fewer Blacks than Whites own their home as opposed to rent their home.

According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. [Round your answers to three decimal places, for example: 0.123]

Compute the probability that a randomly selected peanut M&M is not yellow.



Compute the probability that a randomly selected peanut M&M is green or yellow.



Compute the probability that two randomly selected peanut M&M’s are both red.



If you randomly select five peanut M&M’s, compute that probability that none of them are green.



If you randomly select five peanut M&M’s, compute that probability that at least one of them is green.

An experiment was conducted to study growth characteristics of 8 different provenances (regions of natural occurrence) of Gmelina arborea (a tree native to southern Asia). There are three plots available for planting, so one tree of each provenance is planted in each plot. The response variable is the diameter of each tree (in centimeters) at breast height (1.4 meters above ground).

What type of design is being used in this experiment?

Perform the appropriate analysis to evaluate the differences in mean diameter at breast height of the eight provenances.

Which provenance(s), if any, has (have) largest mean diameter at breast height?

Comment on the effectiveness of the design in increasing the efficiency of the experiment.

A statistical analysis is made of the midterm and final scores in a large course, with the following results:
Average midterm score = 65, SD = 10,
Average final score = 65, SD = 12, r = 0.6
The scatter diagram is football shaped.
a. About what percentage of the class final scores above 70?
b. A student midterm was 75. Predict his final score
c. Suppose the percentile rank of midterm score was 95%, predict his percentile rank on the final score
d. Of those whose midterm score was 70, about what percentage of final scores over 80?

The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 4 years and a standard deviation of 0.4 years. He then randomly selects records on 49 laptops sold in the past and finds that the mean replacement time is 3.8 years.

Assuming that the laptop replacement times have a mean of 4 years and a standard deviation of 0.4 years, find the probability that 49 randomly selected laptops will have a mean replacement time of 3.8 years or less.
P(M < 3.8 years) =  
Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Based on the result above, does it appear that the computer store has been given laptops of lower than average quality?

• Yes. The probability of this data is unlikely to have occurred by chance alone.
• No. The probability of obtaining this data is high enough to have been a chance occurrence.

      With reference to equations (4.2) and (4.3), let Z1 = U1 and Z2 = −U2 be independent, standard normal variables. Consider the polar coordinates of the point (Z1, Z2), that is,

A2 = Z2 + Z2

and   φ = tan−1(Z2/Z1).

1         2

(a)    Find the joint density of A2 and φ, and from the result, conclude that A2 and φ are independent random variables, where A2 is a chi-

squared random variable with 2 df, and φ is uniformly distributed on (−π, π).

(b)    Going in reverse from polar coordinates to rectangular coordinates, suppose we assume that A2 and φ are independent random variables, where A2 is chi-squared with 2 df, and φ is uniformly distributed

on (−π, π). With Z1 = A cos(φ) and Z2 = A sin(φ), where A is the

positive square root of A2, show that Z1 and Z2 are independent,

standard normal random variables.

Please write in BOLD Thanks :)

In Lesson Eight you've learned how to construct confidence intervals for population parameters and proportions, based on data from samples.

1. In a short paragraph, distinguish between Sampling Error and the Margin of Error. Explain what each represents and the relationship between them.
2. In a short paragraph, distinguish between a Point Estimate and an Interval Estimate. Explain what each represents and the relationship between them.
3. In a short paragraph, distinguish between a Confidence Interval and the Level of Confidence. Explain what each represents and the relationship between them.
4. Identify the three components of a Confidence Interval. Explain what each represents and the relationship between them.
5. Describe a potential issue with public opinion polls that report interval estimates, but not confidence intervals. Discuss this in a short paragraph.

Part 2. As a school nutritionist, you are also interested in tracking whether or not children are getting enough calcium in their diet. It is recommended that teenagers consume at least 1,300mg per day of calcium. Assume the average teenager in your school consumes 1,200mg, with a SD of 400mg. 5. Calculate the mean of the sampling distribution for average calcium consumed 6. Calculate the standard error of the mean of that sampling distribution (for samples of 30) 7. Calculate the Z-score associated with 1,300mg of calcium in your sampling distribution 8. For samples of 30 teenagers per class, what is the probability a class average for calcium consumption will fall below the recommended 1,300mg? (Write as decimal, not percentage)

USA Today reported that approximately 25% of all state prison inmates released on parole become repeat offenders while on parole. Suppose the parole board is examining five prisoners up for parole. Let x = number of prisoners out of five on parole who become repeat offenders.

(a) Find the probability that one or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.)


How does this number relate to the probability that none of the parolees will be repeat offenders?

a) These probabilities are the same.

b) This is the complement of the probability of no repeat offenders.    

c) This is twice the probability of no repeat offenders.

d) These probabilities are not related to each other.

e) This is five times the probability of no repeat offenders.

(b) Find the probability that two or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.)


(c) Find the probability that four or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.)


(d) Compute μ, the expected number of repeat offenders out of five. (Round your answer to three decimal places.)
μ = prisoners

(e) Compute σ, the standard deviation of the number of repeat offenders out of five. (Round your answer to two decimal places.)
σ = prisoners

Provide two real-world survey questions that would be useful to you in a professional application or in your everyday life by addressing the following:

(i) Your first should be a question associated with a categorical (qualitative) variable. Explain the measuring scale associated with the question and if the data collected is cross-sectional or time series. What might you be able to infer about the data you would collect?

(ii) Your second should be a question associated with a quantitative variable. Explain the measuring scale associated with the question. Also, determine whether the variable associated with the survey question is discrete or continuous and if the data collected is cross-sectional or time series. What might you be able to infer about the data you would collect?

Be sure to support your statements with logic and argument, citing any sources referenced. Post your initial response early, and check back often to continue the discussion. Be sure to respond to your peers and instructors posts, as well.

The table shows the 2013 per capita total expenditure on health in 35 countries with the highest gross domestic product in that year. Health expenditure per capita is the sum of public and private heath expenditure (in PPP, international $) divided by population. Health expenditures include the provision of health services, family‑planning activities, nutrition activities, and emergency aid designated for health but exclude the provision of water and sanitation.

Make a stemplot of the data after rounding to the nearest $100, so that stems are thousands of dollars and leaves are hundreds of dollars. Split the stems, placing leaves 0 to 4 on the first stem and leaves 5 to 9 on the second stem of the same value.

1) Which numbers are the leaves on the first stem associated with $3000?

A) 13

B) 22356889

C) 5689

D) 137

E) 12355789

F) 611

2) Describe the shape, center, and variability of the distribution.

3) Which country is the high outlier?

4) The distribution is _____, with a single high outlier (______ ). There seem to be two clusters of countries. The center of the distribution is about _______spent per capita. The distribution varies from about _________spent per capita to about _______spent per capita.

Discuss two ways to adjust crude death rate

If a population of college student ages is skewed right, then this indicates?

You wish to test the following claim (H1) at a significance level of α=0.02.

      Ho:μ=52.5
      H1:μ<52.5

You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the population mean is less than 52.5.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 52.5.
• The sample data support the claim that the population mean is less than 52.5.
• There is not sufficient sample evidence to support the claim that the population mean is less than 52.5.

Please explain how to solve on a TI-84 if possible. Thanks!