### Educational Website Content#### Joint Probability Mass Function (pmf) AnalysisA certain market has both an express checkout line and a superexpress checkout line. Let \( X_1 \) denote the number of customers in line at the express checkout at a particular time of day, and let \( X_2 \) denote the number of customers in line at the superexpress checkout at the same time. Suppose the joint pmf of \( X_1 \) and \( X_2 \) is given in the accompanying table.#### Joint PMF of \( X_1 \) and \( X_2 \)| \( X_1 \backslash X_2 \) | 0 | 1 | 2 | 3 ||--------------------------|-------|-------|-------|-------|| 0 | 0.09 | 0.02 | 0.03 | 0.1 || 1 | 0.09 | 0.05 | 0.05 | 0.04 || 2 | 0.06 | 0.1 | 0.08 | 0.04 || 3 | 0.07 | 0.05 | 0.04 | 0.06 |1. **What is \( P(X_1 = 1, X_2 = 1) \)**, that is, the probability that there is exactly one customer in each line? \[ P(X_1 = 1, X_2 = 1) = 0.05 \]2. **What is \( P(X_1 = X_2) \)**, that is, the probability that the numbers of customers in the two lines are identical? \[ P(X_1 = X_2) = \sum_{i=0}^{3} P(X_1 = i, X_2 = i) = 0.09 + 0.05 + 0.08 + 0.06 = 0.28 \]3. Let \( A \) denote the event that there are at least two more customers in one line than in the other line. Express \( A \) in terms of \( X_1 \) and \( X_2 \).

Let X1 denote the number of customers in line at the express checkout at a particular time of…

Answered: x₂ X₂ 0 1 2 3 0.09 0.06 0.04 0.00 1…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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For a particular disease, the probability that a patient passes away within the xth year is given by the following table: xx P(x)P(x) 0 0.016 1 0.031 2 0.256 3 0.298 4 0.35 5 0.028 6 0.021 This means that the probability that someone passes away within the first year is 0.016. The probability that they pass away after one year would be 0.031. What is the mean number of years someone survives? (round to two decimal places) What is the standard deviation for the number of years someone survives? (round to two decimal places) The Range Rule of Thumb for survival would be: years to years. (Round each to two decimal places.) In your own words, interpret what the Range Rule of Thumb tells us about this disease. (If you don't remember what the Range Rule of Thumb is, review the heading "Unusual Values" in the Learning Activities.)
The probability distribution for the number of automobiles sold during a day (x) at Bob Iron Motors is as follows. x f(x) 0 0.001 1 0.007 2 0.034 3 0.099 4 0.188 5 6 0.220 7 0.136 8 0.055 9 0.015 10 0.001 20 The probability that between 3 and 7 automobiles will be sold is, P(3 ≤ x ≤ 7) a 0.852 b 0.869 c 0.887 d 0.905
I. Which of the following are discrete probability distributions? (Yes or No) 1. 4 P(x) 0.10 0.20 0.25 0.40 0.05 2. 2. 3 4 5 P(x) 0.05 0.25 0.33 0.28 0,08 3. 3 4 5 P(x) 0.08 0.25 0.34 0.31 0.04 4. 2 3 4 5 P(x) 0.03 0.22 1.01 0.23 0.02 5. 1 2 3 4 P(x) 0,05 0.27 0.34 0,28 0.06 6. 3 4 5 P(x) 3 3 10 10 10 7. 3 4 P(x) 15 15 8. 3 4 5 P(x) 25 25 25 25 9. 3 4 P(x) 7. 1 10 10 20 20 10. 2. 3 4 5 P(x) 0.212 0.113 0,125 0.224 0.306
0.15 0.4 0.25 A B (i) Calculate the conditional probability that A occurs, given that B has occured. (ii) Calculate P(A'/B)
(50) Let X be a random variable with p.d.f. k 1
In each case, determine the value of the constant c that makes the probability statement correct. (Round your answers to two decimal places.) (a) Φ(c) = 0.9850 (b) P(0 ≤ Z ≤ c) = 0.2995 (c) P(c ≤ Z) = 0.1314 (d) P(−c ≤ Z ≤ c) = 0.6528 (e) P(c ≤ |Z|) = 0.0128 You may need to use the appropriate table in the Appendix of Tables to answer this question.
I. Which of the following are discrete probability distributions? (Yes or No) 1. 3 4 5 P(x) 0.10 0.20 0.25 0.40 0.05 2. 3 4 P(x) 0,05 0.25 0,33 0.28 0,08 3. 4 5 P(x) 0.08 0.25 0.34 0.31 0,04 4. 2 3 4 5 P(x) 0.03 0.22 1.01 0.23 0.02 5. 3 4 5 P(x) 0.05 0.27 0.34 0.28 0.06 6. 2 3 4 5 P(x) 1 3 3 10 10 10 7. 3. 4 P(x) 15 15 8. 2 4 5 6 P(x) 4. 25 25 25 25 9. 3 4 P(x) 1. 3. 20 20 1 10 10 10. 1 3 4 P(x) 0.212 0.113 0.125 0.224 0.306 -
An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is given. y p(y) 0 1 0.50 0.35 0.10 0.05 USE SALT 3 (a) What is the probability that among 25 randomly chosen such individuals, at least 15 have no citations? (Round your answer to three decimal places.) (b) What is the probability that among 25 randomly chosen such individuals, fewer than half have at least one citation? (Round your answer to three decimal places.) What is the probability that among 25 randomly chosen such individuals, the number that have at least one citation is between 10 and 15, inclusive? ("Between a and b, inclusive" is equivalent to (a ≤ x ≤ b). Round your answer to three decimal places.) You may need to use the appropriate table in the Appendix of Tables to answer this question.
Question 2: X ~ Geometric(T) distribution with probability function p(x) = P(X = x) = T(1 – 7)"-1 for x = 1, 2, 3, ... Find P(X x).
Event A is my wife cooking dinner tonight. It has been determined that P(A) = 0.15. What is P(not A)?
a and b

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