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(b) The Atacama Desert in Chile is known as the driest place on Earth. Suppose that in one part of the Atacama Desert, whether it rains at all in a given year has probability 0.2, and whether or not it rains in one year is independent of whether or not it rains in any other year. Answer the following questions, in each case stating clearly the probability model that you use (including the values of any parameters). (i) Suppose that a random variable X is defined to take the value 1 when there is rainfall in a particular year and 0 when there is not. What is the mean of the random variable X? (ii) What is the expected number of years with some rainfall in a period of 100 years? (iii) What is the expected value of the number of years up to and

(b) The Atacama Desert in Chile is known as the driest place on Earth. Suppose that in one part of the Atacama Desert, whether it rains at all in a given year has probability 0.2, and whether or not it rains in one year is independent of whether or not it rains in any other year. Answer the following questions, in each case stating clearly the probability model that you use (including the values of any parameters). (i) Suppose that a random variable X is defined to take the value 1 when there is rainfall in a particular year and 0 when there is not. What is the mean of the random variable X? (ii) What is the expected number of years with some rainfall in a period of 100 years? (iii) What is the expected value of the number of years up to and

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.2: Probability
Problem 3E: The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the...
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All parts of B please
(a) In Question 2(b) of TMA 01, the probability mass function of a discrete random variable X representing the number of bicycles available at a docking station each morning was introduced. This p.m.f. is repeated here, in Table 2. Table 2 The p.m.f. of X x 0 p(x) 0.3 0.2 0.2 0.1 5 6 1 2 3 4 0.1 0.1 0.05 0.05 (i) What is the mean number of bicycles available at the docking station each morning? (ii) What is the variance of the number of bicycles available at the docking station each morning? (b) The Atacama Desert in Chile is known as the driest place on Earth. Suppose that in one part of the Atacama Desert, whether it rains at all in a given year has probability 0.2, and whether or not it rains in one year is independent of whether or not it rains in any other year. Answer the following questions, in each case stating clearly the probability model that you use (including the values of any parameters). (i) Suppose that a random variable X is defined to take the value 1 when there is rainfall in a particular year and 0 when there is not. What is the mean of the random variable X? (ii) What is the expected number of years with some rainfall in a period of 100 years? (iii) What is the expected value of the number of years up to and including the first year in which there is some rainfall?
Transcribed Image Text:(a) In Question 2(b) of TMA 01, the probability mass function of a discrete random variable X representing the number of bicycles available at a docking station each morning was introduced. This p.m.f. is repeated here, in Table 2. Table 2 The p.m.f. of X x 0 p(x) 0.3 0.2 0.2 0.1 5 6 1 2 3 4 0.1 0.1 0.05 0.05 (i) What is the mean number of bicycles available at the docking station each morning? (ii) What is the variance of the number of bicycles available at the docking station each morning? (b) The Atacama Desert in Chile is known as the driest place on Earth. Suppose that in one part of the Atacama Desert, whether it rains at all in a given year has probability 0.2, and whether or not it rains in one year is independent of whether or not it rains in any other year. Answer the following questions, in each case stating clearly the probability model that you use (including the values of any parameters). (i) Suppose that a random variable X is defined to take the value 1 when there is rainfall in a particular year and 0 when there is not. What is the mean of the random variable X? (ii) What is the expected number of years with some rainfall in a period of 100 years? (iii) What is the expected value of the number of years up to and including the first year in which there is some rainfall?
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