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Let X denote the temperature at which a certain chemical reaction takes place. Suppose that X has the given pdf. (1¹(4-x²) -15x52 0 otherwise (a) Sketch the graph of f(x). f(x) • 0.3 0.2 0.1 0.0 (b) Determine the cdf. F(x)= 1.0 0.8 Sketch the cdf. F(x) 0.6 0.4 f(x)=9 0.2 0.0 x -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 O O -1 f(x) 0.20 0.15 SEEb 0.10 0.05 0.00 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 O -1.0 -0.5 0.0 0 3 1 x < = 1 -15x52 X> 2 2 0.25 0.20 0.15 0.10 0.05 f(x) 0.00 O 1.0 F(x) 0.8 0.6 0.4 0.2 0.0 F(X) 1.0 0.8 LIKV 0.6 0.4 0.2 -1 -1 0 S OY is an exponential distribution with parameter 27 OY is a binomial distribution with parameters n=10 and p - 22 OY is an exponential distribution with parameter 2 - 22 1 2 0.0 O 0 1 f(x) 0.5 2 0.4 0.3 0.2 0.1 0.5 1.0 1.5 2.0 C -1.0 -0.5 0.0 0.0 F(X) 1.0 0.8 0.6 0.4 0.2 O 0.0 (c) Is 0 the median temperature at which the reaction takes place? If not, is the median temperature smaller or larger than 0? The median temperature is 0 if and only if F(0) 0.5. Since F(0) -Select--equal 0.5, this --Select--the case. Since F(0) ?0.5, the median must be ---Select--- 0. 0.5 1.0 -1 1 1.5 2.0 2 x (d) Suppose this reaction is independently carried out once in each of ten different labs and that the pdf of reaction time in each lab is as given. Let Y the number among the ten labs at which the temperature exceeds 1. What kind of distribution does Y have? (Give the names and values of any parameters.) OY is a binomial distribution with parameters n 10 and p 돎

Let X denote the temperature at which a certain chemical reaction takes place. Suppose that X has the given pdf. (1¹(4-x²) -15x52 0 otherwise (a) Sketch the graph of f(x). f(x) • 0.3 0.2 0.1 0.0 (b) Determine the cdf. F(x)= 1.0 0.8 Sketch the cdf. F(x) 0.6 0.4 f(x)=9 0.2 0.0 x -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 O O -1 f(x) 0.20 0.15 SEEb 0.10 0.05 0.00 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 O -1.0 -0.5 0.0 0 3 1 x < = 1 -15x52 X> 2 2 0.25 0.20 0.15 0.10 0.05 f(x) 0.00 O 1.0 F(x) 0.8 0.6 0.4 0.2 0.0 F(X) 1.0 0.8 LIKV 0.6 0.4 0.2 -1 -1 0 S OY is an exponential distribution with parameter 27 OY is a binomial distribution with parameters n=10 and p - 22 OY is an exponential distribution with parameter 2 - 22 1 2 0.0 O 0 1 f(x) 0.5 2 0.4 0.3 0.2 0.1 0.5 1.0 1.5 2.0 C -1.0 -0.5 0.0 0.0 F(X) 1.0 0.8 0.6 0.4 0.2 O 0.0 (c) Is 0 the median temperature at which the reaction takes place? If not, is the median temperature smaller or larger than 0? The median temperature is 0 if and only if F(0) 0.5. Since F(0) -Select--equal 0.5, this --Select--the case. Since F(0) ?0.5, the median must be ---Select--- 0. 0.5 1.0 -1 1 1.5 2.0 2 x (d) Suppose this reaction is independently carried out once in each of ten different labs and that the pdf of reaction time in each lab is as given. Let Y the number among the ten labs at which the temperature exceeds 1. What kind of distribution does Y have? (Give the names and values of any parameters.) OY is a binomial distribution with parameters n 10 and p 돎

A First Course in Probability (10th Edition)
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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Let X denote the temperature at which a certain chemical reaction takes place. Suppose that X has the given pdf. - {1² (4-x²) 0 (a) Sketch the graph of f(x). f(x) 0.3 0.20 0.15 hhhh 0.10 0.05 0.00 X -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 0.2 0.1 0.0 (b) Determine the cdf. F(x) = f(x) = 9 1.0 Sketch the cdf. F(X) 0.8 0.6 0.4 -1.0 -0.5 0.0 0.5 0.2 0.0 0 17-(4x - 21/1/2 9 3 1 -1 ≤ x ≤ 2 otherwise + 0 11 3 1.0 1.5 2.0 1 x < -1 -1 ≤x≤ 2 x > 2 2 X O Y is an exponential distribution with parameter > 0.25 0.20 0.15 0.10 0.05 f(x) 0.00 1.0 OY is an exponential distribution with parameter λ = 5 27 0.8 F(x) 0.6 0.4 22 27 0.2 0.0 LKV 0 OY is a binomial distribution with parameters n = 10 and p = 22 27 0 1 2 F(X) 1.0 0.8 0.6 0.4 (c) Is 0 the median temperature at which the reaction takes place? If not, is the median temperature smaller or larger than 0? The median temperature is 0 if and only if F(0) = 0.5. Since F(0) ---Select--- f(x) 0.2 0.0 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 -1 1 2 f(x) equal 0.5, this --Select--- the case. Since F(0) ? 0.5, the median must be -Select--- 0.5 0.4 0.3 0.2 0.1 0.0 F(x) 1.0 0.8 0.6 0.4 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 0.2 0.0 0. -1 0 1 (d) Suppose this reaction is independently carried out once in each of ten different labs and that the pdf of reaction time in each lab is as given. Let Y = the number among the ten labs at which the temperature exceeds 1. What kind of distribution does Y have? (Give the names and values of any parameters.) 5 OY is a binomial distribution with parameters n = 10 and p = 27 2 X X
Transcribed Image Text:Let X denote the temperature at which a certain chemical reaction takes place. Suppose that X has the given pdf. - {1² (4-x²) 0 (a) Sketch the graph of f(x). f(x) 0.3 0.20 0.15 hhhh 0.10 0.05 0.00 X -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 0.2 0.1 0.0 (b) Determine the cdf. F(x) = f(x) = 9 1.0 Sketch the cdf. F(X) 0.8 0.6 0.4 -1.0 -0.5 0.0 0.5 0.2 0.0 0 17-(4x - 21/1/2 9 3 1 -1 ≤ x ≤ 2 otherwise + 0 11 3 1.0 1.5 2.0 1 x < -1 -1 ≤x≤ 2 x > 2 2 X O Y is an exponential distribution with parameter > 0.25 0.20 0.15 0.10 0.05 f(x) 0.00 1.0 OY is an exponential distribution with parameter λ = 5 27 0.8 F(x) 0.6 0.4 22 27 0.2 0.0 LKV 0 OY is a binomial distribution with parameters n = 10 and p = 22 27 0 1 2 F(X) 1.0 0.8 0.6 0.4 (c) Is 0 the median temperature at which the reaction takes place? If not, is the median temperature smaller or larger than 0? The median temperature is 0 if and only if F(0) = 0.5. Since F(0) ---Select--- f(x) 0.2 0.0 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 -1 1 2 f(x) equal 0.5, this --Select--- the case. Since F(0) ? 0.5, the median must be -Select--- 0.5 0.4 0.3 0.2 0.1 0.0 F(x) 1.0 0.8 0.6 0.4 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 0.2 0.0 0. -1 0 1 (d) Suppose this reaction is independently carried out once in each of ten different labs and that the pdf of reaction time in each lab is as given. Let Y = the number among the ten labs at which the temperature exceeds 1. What kind of distribution does Y have? (Give the names and values of any parameters.) 5 OY is a binomial distribution with parameters n = 10 and p = 27 2 X X
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