Mathematics, 18.11.2019 22:31, sjharrison04
Consider the experiment of keeping flipping a fair coin until two heads are flipped consecutively. the outcome is the sequence of the flipped result. possible examples of the outcome include hththh and ttththtthh . the random variable x is defined to be the number of 3 flips of an outcome. for example, x(hththh) = 6 and x(ttththtthh) = 10 . find e(x) . hint: consider three events: f first two flips are , first two 1 = hh f2 = flips are ht , f first flip is . note that , , and form a 3 = t f1 f2 f3 partition of s . the law of total expectation states that e(x) = e(x|f )p(f ) (x|f )p(f ) (x|f )p(f ) , see exercise 1 1 + e 2 2 + e 3 3 7.4.22. try to express e(x|f ) , , and in terms of . 1 e(x|f )2 e(x|f )3 e(x) instead of using the formula of conditional expectation e(x|f) = ∑ (x |f) in exercise 7.4.21, think of as "the r∈x(s) r · p = r e(x|f) expectation of x given that event f occurs."
Answers: 2
Mathematics, 21.06.2019 16:10, bananaslada
Determine whether the following statements are true and give an explanation or counterexample. bold a. when using the shell method, the axis of the cylindrical shells is parallel to the axis of revolution. bold b. if a region is revolved about the y-axis, then the shell method must be used. bold c. if a region is revolved about the x-axis, then in principle it is possible to use the disk/washer method and integrate with respect to x or the shell method and integrate with respect to y.
Answers: 3
Consider the experiment of keeping flipping a fair coin until two heads are flipped consecutively. t...
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