Determining the expected winnings
What is your expected winnings if you win $30 on a roll of a double 6 (dice), and you lose $1 otherwise. (So the random variable X whose expectation you are trying to compute is 30 when you roll a (6,6) and -1 otherwise.)
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Assume that the material is linearly elastic and isotropic. Derive the square-root singular field of a mode III crack. Obtain the stress field and displacement field.
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