stat2303_tutorial03

Compute the expected number of flips that are made

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Unformatted text preview: lipped. Compute the expected number of flips that are made until heads in a row are obtained. Let Let be the number of flips until heads in a row are obtained be the number of flips needed for the first tail, i.e. ~ 1 . If , then the first flips must all be heads. Hence, the number of flips needed for heads in a row will be , i.e. | . If , then the th flip is tail. Hence, the number of flips needed for heads in a row will increase by , i.e. | Therefore, 1 1 1 Note 1 1 1 1 1 1 2 1 1 1 1 Solving 1 1 1 1 1 1 1 1 1 1 1 Page 2 of 3 1 1 1 1 1 1 1 1 1 1 1 Semester 1, 2010­11 STAT2303/2803 Probability Modelling/Stochastic Models 3. If | | Given , for all , show that 0. , | , | | Hence, , | 0 4. If | 1, show that . Note Since | where Hence, | Additionally, | | | | 1 | 1 , 0 1 Therefore, , 5. Show that , , | | . | | | , Page 3 of 3 1 1...
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