Probability & Statistics 1 **Problem 6: Discrete Uniform Distribution**X has a discrete uniform distribution.Given:\[ f(x) = \frac{1}{k}, \, x = 1, 2, \ldots, k \]**Tasks:**i. **Show that the moment generating function (MGF) is:**\[\frac{e^t(1-e^{kt})}{k(1-e^t)}\]ii. **Using the MGF, show that \( E(X) = \frac{k+1}{2} \)**

Introduction: Let X be a discrete random variable, then moment generating function of this variables…

Answered: 6. X has a discrete uniform…

Advanced Engineering Mathematics

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ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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9b In Africa in 2011, the number of deaths of a female from cardiovascular disease for different age groups are in the table below ("Global health observatory," 2013). In addition, the proportion of deaths of females from all causes for the same age groups are also in table below. Table: Deaths of Females for Different Age Groups Age 5-14 15-29 30-49 50-69 Total Cardiovascular Frequency 8 16 56 433 513 All Cause Proportion 0.10 0.12 0.26 0.52 Do the data show that the death from cardiovascular disease are in the same proportion as all deaths for the different age groups? Test at the 5% level. (iv) Are any of the expected frequency values (for which HO is true) for any cell in your table less than 5? Calculate the expected frequencies using technology, the select most correct answer: A. yes - this will not affect results of hypothesis test B. yes - this may invalidate results of hypothesis test C. no - this will not affect…
9a In Africa in 2011, the number of deaths of a female from cardiovascular disease for different age groups are in the table below ("Global health observatory," 2013). In addition, the proportion of deaths of females from all causes for the same age groups are also in table below. Table: Deaths of Females for Different Age Groups Age 5-14 15-29 30-49 50-69 Total Cardiovascular Frequency 8 16 56 433 513 All Cause Proportion 0.10 0.12 0.26 0.52 Do the data show that the death from cardiovascular disease are in the same proportion as all deaths for the different age groups? Test at the 5% level. (i) Which of the following statements correctly defines the null hypothesis HO? A. Deaths from cardiovascular disease in females are not in the same proportion as all deaths for the different age groups B. Deaths from cardiovascular disease in females are in the same proportion as all deaths for the different age groups C. neither of…
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Number oF Students Number oF Class boundary Kilograms 56- 59 52-55 48 - 51 44-47 4 40-43 3
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Chart Based Probability Section Rubber Balls in a Box Setup Stars | Stripes | Dots Red 8 15 12 Blue 7 3 14 Green 9 6. Experiment: The rubber balls all have the same size, texture, weight, etc. They cannot be distinguished without looking at them. The rubber balls are mixed around thoroughly in the box. One rubber ball is to be drawn randomly. Let X = the color on the rubber ball. Let Y = the pattern on the rubber ball. 2. Use the rubber bals in a box setup. Find P( X= Green ). This is a short answer question. The correct answer is a fully simplified fraction.
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Dimensional characteristics, such as height, are an example of a: a. continuous random variable b. discrete random variable c. categorical random variable d. Any of the above
9c In Africa in 2011, the number of deaths of a female from cardiovascular disease for different age groups are in the table below ("Global health observatory," 2013). In addition, the proportion of deaths of females from all causes for the same age groups are also in table below. Table: Deaths of Females for Different Age Groups Age 5-14 15-29 30-49 50-69 Total Cardiovascular Frequency 8 16 56 433 513 All Cause Proportion 0.10 0.12 0.26 0.52 Do the data show that the death from cardiovascular disease are in the same proportion as all deaths for the different age groups? Test at the 5% level. (vii) Comparing p-value and α value, which is the correct decision to make for this hypothesis test? A. Reject Ho B. Fail to reject Ho C. Accept Ho D. Accept HA Enter letter corresponding to correct answer. (viii) Select the statement that most correctly interprets the result of this test: A. The result is not statistically…
Walmart Revenue The annual revenue of Walmart is given in the table below (source ). Walmart Annual Revenue (Billions of US dollars) 559.151 Year 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 523.964 514.405 500.343 485.873 482.130 485.651 476.294 468.651 446.509 421.849 408.085 404.254 377.023 348.368 312.101 284.310 Apply linear regression to the data in the table to find a model y = mx + b, where y is Walmart's annual revenue in billions of US dollars, and a is the number of years since 2000. Use the model y = mx + b with m rounded to the nearest tenth and 6 rounded to the nearest

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6. X has a discrete uniform distribution fix) = 1/k, x= 1, 2, ., k. i. Show that the moment generations function (MGF) is e(- kC1-et ii. Using the MGF show that E(X) =