Unformatted text preview: be tested one at a time (without replacement) until the defective one is identiﬁed. Let X be the number of tests made until the ﬁrst defective one is found (including the test that identiﬁes the ﬁrst defective one). Let Y be the number of additional tests up to and inlcuding the time that the second defective transistor is found. Find the joint pmf of ( X,Y ). The following problems are optional for students enrolled in 360, required for students enrolled in 560. Problem 5. Suppose X is uniformly distributed on the range [0 , 1]. Find the probability that X is irrational, ie, ﬁnd P [ X / ∈ Q ]. Problem 6. Again, suppose X ∼ U (0 , 1). Let Y n be the random variable given by Y n = 1 n d nX e , where d x e denotes the least integer k such that x ≤ k . (a) Find the distribution of Y n . (b) Find the distribution of Z n := Y n-X ....
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- Fall '07
- Probability distribution, Probability theory, Randomness, Discrete probability distribution, certain engineering class