A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Question
The genotype of an organism can be either normal (wild type) or mutant. Each generation, a wild 5C'ype individual has probability 0.03 of having a mutant offspring, and a mutant has probability 0.005 of having a wild type offspring. Suppose that initially 0.9 of the population is wild type and 0.1 is mutant. What fraction of the population is wild type after 1 generation? After 2 generations? The nAChR ion channel can be in one of three states: resting (R), closed with Ach bound (C), and open (0) with transition probabilities (per one microsecond): 0.04 (from R to C), 0.07 (from C to R), 5D 0.12 (from C to O) and 0.02 (from O to C); the other transition probabilities are 0. Suppose that initially 3/4 of ion channels are in R and 1/4 are in C. What fraction of the ion channels is open after 1 microsecond? After 2 microseconds? There are three kinds of vegetation in an ecosystem: grass, shrubs, and trees. Every year, 25% of grassland plots are converted to shrubs, 20% of shrub plots are converted to trees, 8% of trees are 5E onverted to shrubs, and 1% of trees are converted to grass; the other transition probabilities are 0. Suppose that initially the ecosystem is evenly split: 1/3 grass, 1/3 shrubs and 1/3 trees. What fraction of ecosystem is covered in shrubs after 1 year? after 2 years?
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Transcribed Image Text:The genotype of an organism can be either normal (wild type) or mutant. Each generation, a wild 5C'ype individual has probability 0.03 of having a mutant offspring, and a mutant has probability 0.005 of having a wild type offspring. Suppose that initially 0.9 of the population is wild type and 0.1 is mutant. What fraction of the population is wild type after 1 generation? After 2 generations? The nAChR ion channel can be in one of three states: resting (R), closed with Ach bound (C), and open (0) with transition probabilities (per one microsecond): 0.04 (from R to C), 0.07 (from C to R), 5D 0.12 (from C to O) and 0.02 (from O to C); the other transition probabilities are 0. Suppose that initially 3/4 of ion channels are in R and 1/4 are in C. What fraction of the ion channels is open after 1 microsecond? After 2 microseconds? There are three kinds of vegetation in an ecosystem: grass, shrubs, and trees. Every year, 25% of grassland plots are converted to shrubs, 20% of shrub plots are converted to trees, 8% of trees are 5E onverted to shrubs, and 1% of trees are converted to grass; the other transition probabilities are 0. Suppose that initially the ecosystem is evenly split: 1/3 grass, 1/3 shrubs and 1/3 trees. What fraction of ecosystem is covered in shrubs after 1 year? after 2 years?
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