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ty distribution:
x 3 5 8 10
pX(x) k k k 2k
i. Determine the constant k and hence write down the probability
distribution of X.
ii. Find E(X), the expected value of X.
iii. Find Var(X), the variance of X.

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y aces or twos, you lose the game immediately. You also lose if you draw picture cards(J,Q,K) more than twice. In this question, you’ll study the probability of winning this game.(a) What is the probability of drawing no aces or twos after thirteen draws?(b) Given you have drawn thirteen times, none of which is aces or twos, what is the probability that you draw at most two picture cards?(c) What is the probability to win this game?
12. Suppose you are tossing an unbiased coin for100times.(a) What is the probability of getting50heads and50tails?(b) LetXbe the random variable counting the number of heads you observe in this exper-iment. What is the expected value ofX? What is the variance ofX? What is thestandard deviation ofX?
13. The following are probability distributions for two random variablesX,Y.
kPr(X=k)
0,0.4
1,0.3
2,0.3
kPr(Y=k)
0,0.5
1,0.3
2,0.2
(a) Construct the probability distribution table for the random variableXY.(b) Find E[X],E[Y] and E[XY]. Is is true that E[XY] =E[X]E[Y]?(c) Find the variances σ2X,σ2Y,σ2XY of X,Y and XY. Is it true that σ2XY=σ2Xσ2Y?
14. The aliens who are fond of gambling came back to play another game with you. In this game, you first toss a coin5times. If you observe3or fewer tails, you roll a die3times. If youobserve4or more tails, you roll a die20times. What is the probability that you end up with at most two6’s in your dice rolls?
15. (Challenge question, worth2points) You have two bags, each of which contains10marbles.Each time you remove a marble from a random bag. What is the probability that after one of the bags is emptied, there are still exactly3marbles in the other bag?

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- 1); I{x>1}, theta > 1.
(a) Show that log Xi has an exponential distribution with a mean of 1/theta.
(b) Find the form for a UMP test of H_0: theta <= theta_0 vs. H_a : theta > theta_0.
(c) Give formula for nding the rejection region for a given value of alpha.
Hint: use the result from (a) to find the distribution of the test statistic.
(d) Conduct the test in (b) with alpha = 0.05 and theta_0 = 1:5 using the dataset: {1.2, 2.4, 1.3, 1.7, 1.9}.
(e) Find the form of a UMPU test for testing H_0 : theta = theta_0 vs. H_a : theta_0 != theta_0.
(f) Use the data in (d) to conduct the test in (e) with alpha = 0.05 and theta_0 = 1.5.

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- 1); I{x>1}, theta > 1.
(a) Show that log Xi has an exponential distribution with a mean of 1/theta.
(b) Find the form for a UMP test of H_0: theta <= theta_0 vs. H_a : theta > theta_0.
(c) Give formula for nding the rejection region for a given value of alpha.
Hint: use the result from (a) to find the distribution of the test statistic.
(d) Conduct the test in (b) with alpha = 0.05 and theta_0 = 1:5 using the dataset: {1.2, 2.4, 1.3, 1.7, 1.9}.
(e) Find the form of a UMPU test for testing H_0 : theta = theta_0 vs. H_a : theta_0 != theta_0.
(f) Use the data in (d) to conduct the test in (e) with alpha = 0.05 and theta_0 = 1.5.

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- 1); I{x>1}, theta > 1.
(a) Show that log Xi has an exponential distribution with a mean of 1/theta.
(b) Find the form for a UMP test of H_0: theta <= theta_0 vs. H_a : theta > theta_0.
(c) Give formula for nding the rejection region for a given value of alpha.
Hint: use the result from (a) to find the distribution of the test statistic.
(d) Conduct the test in (b) with alpha = 0.05 and theta_0 = 1:5 using the dataset: {1.2, 2.4, 1.3, 1.7, 1.9}.
(e) Find the form of a UMPU test for testing H_0 : theta = theta_0 vs. H_a : theta_0 != theta_0.
(f) Use the data in (d) to conduct the test in (e) with alpha = 0.05 and theta_0 = 1.5.

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erest to this study.
Needless to say, this sales strategy will be effective when the distribution channels for the product in question are well planned, when there is sufficient advertising to let the consumers know about the promotion, when the package clearly indicates the coupon redemption scheme with the expiration date, if any, and the packaging of the product is of the right size (neither too big nor too small to serve the needs of the consumer). Of course, all these factors will not help, unless there is an established frequent need for the product for consumers.
Develop a theoretical framework for the above mentioned scenario.
(5 marks)
Ques. 14
Read the following information identify the concepts and develop a conceptual model for the scenario below.
Incidence of smoking in movies has started to increase again, after having declined for several decades. According to the National Cancer Institute smoking is seen in at least three out of four contemporary box office hits. What's more, identifiable cigarette brands appeared in about one-third of all movies in 2019. Exposure to smoking in movies is an important predictor of adolescent smoking initiation: smoking in movies has been shown to affect adolescents' intentions to start smoking. In turn, the intentions to start smoking are determined by a more positive attitude toward smoking after seeing a film character smoke. Recent research has revealed that the relationship between seeing a film character smoke and the attitude toward smoking is stronger when a person's identification with a film character increases. These findings are consistent with social learning theory, which predicts that attitudes and behaviors are modeled by observing the behaviors of others.
HELP URGENT PLZ
RESEARCH SUBJECT
QUESTION IS NOT INCOMPLETE OR MISSING
1)Dorothy Dunning , Chief Production Manager , was on top of the world just two years ago . In her nontraditional job , she was cited to be the real backbone of the company , and her performance was in no small measure responsible for the mergers the institution was contemplating with other well - known global corporations . Of late though , the products of the company had to be recalled several times owing to safety concerns . Quality glitches and production delays also plagued the company . To project a good image to consumers , Dunning developed a very reassuring web site and made sweeping changes in the manufacturing processes to enhance the quality of the product , minimize defects , and enhance the efficiency of the workers , A year after all these changes , the company continues to recall defective products !
Do you think so research might have solved the Dorothy problem , if yes how ? (Be specific while answering and plan the body of writing recalling the concept of research ) 3marks
2) The GAAP ( Generally Accepted Accounting Principles ) do an unacceptable job of accounting for the principal activities of the Information Age companies . Today , investors are in the dark because the accounting is irrelevant . The basic purpose of accounting is to provide useful information to help investors make rational investment , credit , and similar decisions , but today's most important assets and activities - intellectual capital and knowledge work are totally ignored . Professor Robert A. Howell wants to reform the accounting system with the goal of making clear the measurement of how companies produce cash and create value .
How would you define the problem in the following case ? 2 MARKS

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standard deviation $100. Approximately what percentage of the painting have value between $800 and $1000?

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ch as 44,46,48,50,52,54,56 ..
1) determine what percent of the students are taller than 55 inches?
2) determine cut off value for the shortest 25% ? (round your answer for 2 to 4 decimals) ?

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9.Let's say that I have a data set of every time a certain person has coughed since the beginning of ...

his year. I'm looking for a formula that will tell me the probability that a person will cough x number of times in a given week.
I started with the Poisson Distribution, but Poisson doesn't seem to take into account standard deviation. To calculate the probability with Poisson, only the mean, expected value, and test value are needed, meaning the variance/standard deviation of the data could vary widely, and you'd still get the same probability distribution. For example, if someone coughed exactly 5 times everyday, you'd get the same probability distribution if this person alternated coughing 0 times one day, 10 times the next, 0 times the next day, 10 times the next, and so on.
Does my question make sense? Thanks for your help.

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s, you run the following re- gression on a sample of 65 countries for the year 2012:
books = 8.2314 + (1.0329)
+ 0.3149 age (0.4111)
8.1391 (0.5812)
?
income
4.8121 (0.3543)
+
ereaders,
3.4125 educ (0.7314)
where books is the number of paperback novels purchased in 2012, income is per capita GDP in 2012, educ is the average number of years of education for the population in 2012, age is the average age of the population in 2012 and ereaders is the number of electronic readers (e.g. Kindles) sold in 2012. The numbers in parentheses refer to standard errors corresponding to the estimated coefficients. You also find that R2 = 0.7231 and SSR = 1, 231.
(a) Which of the slope coefficients are statistically different from zero at the 5% level of significance? Perform statistical tests to answer this question. [8 marks]
Solution: Each test carries 2 marks. t ratios are: 14.0039, 4.66, 0.7659, -13.5819. The 2.5% critical value for a tn?k=65?5=60 distribution can be seen to be 2.0000, implying that all coefficients except the one on age are significant.
(b) Does the intercept have a plausible interpretation? Explain briefly. [4 marks]
Solution: The intercept indicates that demand for paperback novels equals 8.2314 when income, educ, age and ereaders all equal zero. Clearly this is not plausible.
(c) Construct a 95% confidence interval for the coefficient on age. [8 marks]
Solution: CI is given by [bage

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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics