Concrete experiences a characteristic marked increase in “creep” when it is heated for the first time under load. An experiment was conducted to investigate the transient thermal strain behavior of concrete (Magazine of Concrete Research, Dec. 1985). Two variables thought to affect thermal strain are X, rate of heating (degrees centigrade per minute), and Y, level of load (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 as given in the table. Suppose a concrete specimen is randomly selected from among those in the experiment that yielded acceptable thermal strain behavior.

a. Find the probability that the concrete specimen was heated at a rate of .3°C/minute.

b. Given that the concrete specimen was heated at .3°C/minute, find the probability that the specimen had a load of 20%.

c. Are rate of heating X and level of load Y correlated?

d. Are rate of heating X and level of load Y independent?

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X(°C/minute) .1 .2 .3 .4 .5 .17 .11 .07 .05 .05 Y 10 .10 .06 .05 .02 .01 20 .09 .04 .03 .01 30 .08 .04 .02 0 0