1. (20 points) The discrete random variables X and Y have the joint probability
ID: 3366771 • Letter: 1
Question
1. (20 points) The discrete random variables X and Y have the joint probability mass shown below 0 0.08 .(6 points) Find the expected value of X, E0)? (8 points) Find the expected value of XY,E(XY)? * .(6 points) Find the covariance of X and Y. Covpx, during any oiven hour. If a random sampling of 10 cars approaching the intersection is ma (20 points) At an automotive facility, engineers are proposing to use a tungsten rod as part of a (20 points) At a common intersection, the probability of a car making a loft hand turn is 0.25 the next hour (10 points) What is the probability that less than three cars make a left turn? b. (15 points) How many cars should be expected that do NOT turn left? mechanical assembly. The design of this assembly requires (on average) that the part be capabie of carrying 37,000 pounds. If the average tensile strength of an experimental sampling of 33 specimens of tungsten rod is measured to be 40,000 lbs with a standard deviation of 3,750 lbs, will 95% of these and show all calculations. (Hint: make a sketcht) specimens meet the design average tensile strength? State any assumptions 4. (20 points) A student has a class that is supposed to end at 9:00AM and another that is supposed to begin at 9:10AM. Suppose the actual ending time of the first class is a normally distributed random variable, A, with mean of 9:02 and standard deviation of 1.5 min. Suppose also that the actual starting time of the second class is a normally distributed also that the travel time between classrooms is also a normally distributed random var random variable, B, with a mean of 9:10 and standard deviation of 1.0 minutes. Suppose C, with mean of six minutes and standard deviation of 1.0 minutes. What is the probability independence of A, B, and C (which is reasonable if the student pays no attention to the that the student makes it to the second class before the lecture starts? Assume finishing time of the first class). Hint: Create a relationship between these three variable, and then use the rules you have learned. 5. (20 points) The desired percentage of Si0, in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO2 in a sample is normally distributed with ? 0.3 and the sample mean is 5.25. Does this indicate conclusively that the true average percentage differs from 5.5? Justify your answer and clearly state your null and alternate hypotheses for this test. Perform your test for a significance level of 0.01Explanation / Answer
1. From the given data
a) E(X) = 0*0.57 + 1*0.43 = 0.43
b) E(XY) = (0)(0)0.1 + 0*1*0.22 + 0*2*0.25 + 1*0*0.16 + 1*1*0.19 + 1*2*0.08 = 0.35
c) E(Y) = 0*0.26 + 1*0.41 * 2*.33 = 1.07
Cov(X,Y) = 0.35 - 1.07 * 0.43 = -0.1101
XY 0 1 2 Total 0 0.1 0.22 0.25 0.57 1 0.16 0.19 0.08 0.43 Total 0.26 0.41 0.33 1Related Questions
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