” 辅导MSBA7003编程、 写作Analysis程序语言、 写作Java，Python编程MSBA7003 Quantitative Analysis MethodsAssignment 1 (Due October 5 at 09:00 a.m.; Please submit your solutions with the template.)Q1.The joint probability distribution among three random variables (X, Y, and Z) is given in thefollowing tables.Z = 0 Z = 1X = 0 X = 1 X = 0 X = 1Y = 0 0.18 0.12 Y = 0 0.064 0.096Y = 1 0.18 0.12 Y = 1 0.096 0.144Which of the following statement(s) is(are) true?(A) X = 0 and Y = 0 are unconditionally independent.(B) Given Z = 0, the two events X = 1 and Y = 1 are independent.(C) E[ X Y | Z = 1 ] = 0.096.(D) P( Z = 1 | X = 0 ) = 0.16.(E) None of the above.Q2.According to the Venn diagram below, which of the following statement(s) is(are) true?(A) Event A and event B are dependent without knowing event C.(B) Given that C occurred, A and B are independent.(C) P(BC) = P(BC|A).(D) Without knowing B, event A and event C are independent.(E) None of the above.Q3.ABC Inc. is considering launching a new product and there are two options: product X andproduct Y. Product X requires an initial investment of $15 million and product Y requires $5million. The total profit (before subtracting the initial investment) that can be generated byeach product depends on the market condition. If the market is strong, product X can generatea total profit of $100 million and product Y can generate $20 million; if the market is weak,product X will lead to a net loss of $80 million and product Y will cause a net loss of $9 million(before subtracting the initial investment). However, the company has no idea about theprobability of a strong market. The probability of a strong market can be 0.2 or 0.5 or 0.8, andthey are equally likely.To get a better understanding of the market before deciding the choice of the new product, themanager hired a consulting firm to conduct a market research. According to historical data, thisconsulting firm can successfully predict a strong market in 65% cases and can correctly predict aweak market in 55% cases. This time, their report gave a favorable conclusion.Based on this information, which of the following statement(s) is(are) true?(A) If the consulting firm is not hired, it is better not to introduce any product.(B) Given the favorable report, the expected probability of a strong market is about 0.522.(C) Given the favorable report, ABC should introduce product X.(D) The expect value of the consulting firms report is about $0.1259 million.(E) None of the above.Q4.For the Googles interview question, which of the following statement(s) is(are) true?(A) The expected minimum number of tries is 3.(B) The expected minimum number of tries is 4.(C) The expected minimum number of tries is 5.(D) The expected minimum number of tries is 6.(E) None of the above.Q5.You are testing the quality of light bulbs made by a manufacturer. The life span follows anexponential distribution with an unknown mean. There are three possibilities for the mean lifespan: high quality (2 years), medium quality (1 year), and low quality (half a year). They areequally likely at the beginning. You sampled three light bulbs for a half-year period. The firstone lasts for half a year and is still working; the second one lasted for less than one month (i.e.,1/12 years); the third one lasts for half a year and is still working.Based on this information, which of the following statement(s) is(are) true?(A) The mean life span is less than 1 year.(B) The light bulbs are most likely to be of medium quality.(C) At the beginning, the probability that a light bulb can last for more than half a year is 0.42.(D) After observing the samples, the probability that a light bulb can last for more than half ayear is 0.45.(E) None of the above.如有需要，请加QQ：99515681 或邮箱：99515681@qq.com
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