Which of the following statements are true?O a. Chebychev's inequality generally requires the random variable X to be non-negative.O b. Probabilities are always less or equal than 1.O c. Markov's inequality generally requires the random variable X to be non-negative.O d. Probability density functions are always less or equal than 1.

Markov inequality: If X is a nonnegative random variable and a > 0, then the probability that X…

Answered: Which of the following statements are…

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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Two wine tasters rate each wine they taste on a scale of 1 to 5. From data on their ratings of a large number of wines, we obtain the given probabilities for both tasters' ratings of a randomly chosen wine. Taster 2 Taster 1 1 2 3 4 5 11 0.050.05 0.020.02 0.010.01 0.000.00 0.000.00 22 0.020.02 0.080.08 0.020.02 0.020.02 0.010.01 33 0.010.01 0.020.02 0.240.24 0.050.05 0.010.01 44 0.000.00 0.020.02 0.050.05 0.230.23 0.020.02 55 0.000.00 0.010.01 0.010.01 0.020.02 0.080.08 (c) What is the probability that Taster 11 rates a wine higher than Taster 2? Give your answer to two decimal places. probability:
A truth serum has the property that 93% of the guilty suspects are properly judged while, of course, 7% of the guilty suspects are improperly found innocent. On the other hand, innocent suspects are misjudged 3% of the time. If the suspect was selected from a group of suspects of which only 7% have ever committed a crime, and the serum indicates that he is guilty, what is the probability that he is innocent? Use Bayes Theorem to solve this question. The probability that the suspect is innocent is (Round to four decimal places as needed.)
Suppose that we have a sample space S = {E₁, E2, E3, E4, E5, E6, E7], where E₁, E2, ..., E7 denote the sample points. The following probability assignments apply: P(E₁) = 0.20, P(E₂) = 0.05, P(E3) = 0.20, P(E4) = 0.15, P(E5) = 0.25, P(E6) = 0.05, and P(E7) = 0.10. Let A = {E₁, E4, E6} B = {E2, E4, E7} C = {E2, E3, E5, E7}. Find P(AC). 0.7000 0.6000 0.3000 0.5714 O 0.4000 Question 3
Daily sales records for a car dealership show that it will sell 0, 1, 2, or 3 cars, with probabilities 0.3, 0.5, 0.15, 0.05 respectively let X be the number of sales in a 2-day period, assuming that the sales are independent from day to day. The probability that two or more sales are made in the next 2 days is
Assume that 12 jurors are randomly selected from a population in which 80% of the people are Mexican-Americans. Refer to the probability distribution table below and find the indicated probabilities. xx P(x)P(x) 0 0+ 1 0+ 2 0+ 3 0.0001 4 0.0005 5 0.0033 6 0.0155 7 0.0532 8 0.1329 9 0.2362 10 0.2835 11 0.2062 12 0.0687 Find the probability of exactly 7 Mexican-Americans among 12 jurors. Round your answer to four decimal places.P(x=7)=P(x=7)= Find the probability of 7 or fewer Mexican-Americans among 12 jurors. Round your answer to four decimal places.P(x≤7)=P(x≤7)= Does 7 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans? no yes
If two events are statistically independent, then the probability that they both occur is: a. 0 b. 0.5 c. 1.0 d. the product of their marginal probabilities e. cannot be determined with the information given.
Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs. Suppose that the probability distribution of y is as follows. y 0 1 2 3 4 p(y) 0.63 0.19 0.11 0.05 ? (a) Only y values of 0, 1, 2, 3, and 4 have positive probabilities. What is p(4)? (Hint: Consider the properties of a discrete probability distribution.) p(4) = Calculate P(y ≤ 2), the probability that the carton contains at most two broken eggs. P(y ≤ 2) = Calculate P(y < 2), the probability that the carton contains fewer than two broken eggs. P(y < 2) =
Let S be the educational attainment of individuals in a town, with values S-0 for less than high school and S=1 for high school or above. Also, let Y be their individual annual income with values Y-O for less than $20,000, Y-1 for between $20,000 and $40,000, and Y=2 for above $40,000. Consider now the following joint probabilities: Y-0 (less than $20K) Y-1 ($20K-$40K) Y-2 (more than $40K) 0.03 0.01 0.36 0.33 SIY S-0 (Less than HS) 0.05 Y-1 (HS or more) 0.22 Determine the conditional standard deviation of the level of educational attainment given that the individual annual income is between $20,000 and $40,000.
Consider three classes (I, II and III) consisting of 30, 25, and 45 students. Suppose a student is selected from class I, then he has 10% chance to make an A. Assume that these probabilities for the class II and III are 15% and 20% respectively. If a student is selected randomly and has an A, what is the probability that he is from class III. Enter your answer to the nearest FOUR decimal places. 0.5715
Flat screen TVs require high quality glass with very few flaws. A television manufacturer receives glass panels from two different suppliers. Let x and y denote the number of flaws in a randomly selected glass panel from the first and second suppliers, respectively. Suppose that the probability distributions for x and y are as follows. 1 2 3 4 p(x) 0.4 0.3 0.2 0.1 y 1 2 3 4 P(y) 0.2 0.6 0.2 The mean values of both x and y are 1. However, the probability distribution for the second supplier is concentrated closer to the mean value than is the first supplier's distribution. If the manufacturer wanted to select a single supplier for glass panels, which of these two suppliers would you recommend? Justify your choice based on consideration of both center and variability. O The two suppliers are equal in terms of center, however the the greater variability in the first distribution tells us that it is more consistent. Thus the first supplier should be recommended. O The two suppliers are…

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