A biased coin having probability p of landing heads is tossed repeatedly, with the outcomes of successive tosses being independent. 1. Let X be the number of heads in the first 5 tosses. Find P (X= 2) to three decimal places when p = 14. (a) 0.264; (b) 0.088; (c) 0.313; (d) 0.897; (e) none of these. 2. Let Y be the number of heads in the first 100 tosses. Using an appropriate approximate distribution, find P (Y ≤ 2) to three decimal places when p = 150. (a) 0.639; (b) 0.168; (c) 0.500; (d) 0.677; (e) none of these. 3. Let Z be the number of tails before the first head occurs. Find E[Z] when p = 13. (a) 3; (b) 2; (c) 3 2 ; (d) 1 2; (e) none of these.

A biased coin having probability p of landing heads is tossed repeatedly, with the outcomes of successive tosses being independent. 1. Let X be the number of heads in the first 5 tosses. Find P (X= 2) to three decimal places when p = 14. (a) 0.264; (b) 0.088; (c) 0.313; (d) 0.897; (e) none of these. 2. Let Y be the number of heads in the first 100 tosses. Using an appropriate approximate distribution, find P (Y ≤ 2) to three decimal places when p = 150. (a) 0.639; (b) 0.168; (c) 0.500; (d) 0.677; (e) none of these. 3. Let Z be the number of tails before the first head occurs. Find E[Z] when p = 13. (a) 3; (b) 2; (c) 3 2 ; (d) 1 2; (e) none of these.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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