Question

1. An experiment was conducted to investigate the transient thermal strain behavior of concrete. Two variables thought to affect thermal strain are X, rate of heating (degrees centigrade per minute), and Y, level of lowa (percentage of initial strength) Concrete specimens are prepared and tested under various combinations of heating rate and load, and the thermal strain is determined for each. Suppose the joint probability distribution for X and Y for those specimens that yielded acceptable results is given in the table below. Suppose a concrete specimen is randomly selected from among those in the experiment that yielded acceptable thermal strain behavior 0.2 0.3 0 0.17 0.11 0.07 005 0.05 10 0.1 0.06 0.05 0.02 0.01 0.1 0.4 0.5 20 0.09 0.04 0.03 0.01 30 | 0.08 0.04 0.02 What is the marginal probability distribution for X and Y? (5 points) a. b. Given that the concrete specimen was heated at 0.3°C/minute, find the probability that the specimen had a load of 20%. (5 points) Find the coefficient of correlation and determine if heating rate X and level of load Y correlated? IThe ollowing page was left blank to provide more space for your work, (15 points)

Answer 1

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