What are the probability distribution of X and Y? Are they independent?
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Assume that the joint
| 1 | 2 | 3 | |
| 1 | 0.32 | 0.03 | 0.01 |
| 2 | 0.06 | 0.24 | 0.02 |
| 3 | 0.02 | 0.03 | 0.27 |
What are the probability distribution of X and Y? Are they independent?
Since ,the joint probability distribution of X and Y is given by,
| 1 | 2 | 3 | Total | |
| 1 | 0.32 | 0.03 | 0.01 | 0.36 |
| 2 | 0.06 | 0.24 | 0.02 | 0.32 |
| 3 | 0.02 | 0.03 | 0.27 | 0.32 |
| Total | 0.40 | 0.30 | 0.10 |
Our aim is to find the probability distribution of X and Y.
Are X and Y independent ?
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Solved in 2 steps
- Data were collected from a survey given to graduating college seniors on the number of times they had changed majors. From that data, a probability distribution was constructed. The random variable X is defined as the number of times a graduating senior changed majors. It is shown below: 1 3 4 8 P(X = x) |0.252 0.286 0.13 0.188 0.082 0.038 0.02 0.003 0.001 a. What is the probability that a randomly selected student changed his or her major at least once? b. What is the probability that a randomly selected student changed his or her major at most twice? c. Given that a randomly selected person did change majors, what is the probability that he or she changed majors more than three times? (Round your answer to three decimal places.)The table below shows the grade distribution for a section in 6 classes. Determine if each of the distributions 1-6 are valid probability distributions or not and explain your reasoning. Distribution A B C D E 1 0.3 0.3 0.3 0.2 0.1 2 0 0 1 0 0 3 0.3 0.3 0.3 0 0 4 0.3 0.5 0.2 0.1 -0.1 5 0.2 0.4 0.2 0.1 0.1 6 0 -0.1 1.1 0 0Suppose that the random variable x, shown below, represents the number times. P(x) represents the probability of a randomly selected person having received that number of speeding tickets during that period. Use the probability distribution table shown below to answer the following questions. 43 x P(x) = 0 1 2 3 > Next Question 4 5 6+ 0.2951 0.2587 0.1924 0.1604 a) What is the probability that a randomly selected person has received five tickets in a three-year period? P(x = 5) 0.0492 0.0442 0.0000 b) What is the probability that a randomly selected person has received one tickets in a three-year period? P(x = 1) = c) What is the probability that that a randomly selected person has received more than zero tickets in a three- year period? P(x > 0) d) What is the probability that that a randomly selected person has received one or less tickets in a three-year period? P(x ≤ 1) =
- Does the following table represent a valid discrete probability distribution? 1 2 4 5 P(X= x) 0.11 0.06 0.18 0.06 0.59 3.Let X = {Email, In Person, Instant Message, Text Message}; P(Email) = 0.06 P(In Person) = 0.55 P(Instant Message) = 0.24 P(Text Message) = 0.15 Is this model a probability distribution? A. Yes. B. No. C. Maybe.High school students in Michigan sometimes get "snow days" in the winter when the roads are so bad that school is canceled for the day. Define the random variableX = the number of snow days at a certain high school in Michigan for a randomly selected school year. Suppose the table below gives the probability distribution of X. 1. Value x, 1. 3 4 5 6 7 8 9 10 Probability p, ? 0.19 0.14 0.10 0.07 0.05 0.04 0.04 0.02 0.01 0.01 (a) Write the event “the school year has O snow days" in terms of X. Then find its probability. (b) At this high school, if more than 5 snow days are used over the course of the year, students are required to make up the time at the end of the school year. What's the probability that a randomly selected school year will require make-up days?
- The following table lists certain values of x and their probabilities. Verify whether or not it represents a valid probability distribution. P(x) 0 0.31 1 0.30 2 0.19 3 0.16 The table a valid probability distribution.[Item#6] Please provide proper and complete solution. I won't like your answer if it is INCOMPLETE! 6. Sixty percent of news articles posted on the popular social media app FacePalm are fake. Assuming that 60% of the news in your newsfeed in FacePalm are indeed fake and you randomly select a news article (selections are independent from one another), what is the probability that: A. the first legitimate news articles you find is the 8th news articles you selected? B. the first legitimate news articles you find is the 4th or 3rd news articles you selected? C. the first legitimate news articles you find is among the first 6 news articles you selected?Benford's law, also known as the first-digit law, represents a probability distribution of the leading significant digits of numerical values in a data set. A leading significant digit is the first occurring non-zero integer in a number. For example, the leading significant digit in the number 127 is 1. Let this leading significant digit be denoted x. Benford's law notes that the frequencies of x in many datasets are approximated by the probability distribution shown in the table. 1 3 4 5 7 8 9. P(x) 0.301 | 0.176 | 0.125 | 0.097 0.079 | 0.067 0.058 0.051 | 0.046 Determine E(X), the expected value of the leading significant digit of a randomly selected data value in a dataset that behaves according to Benford's law? Please give your answer to the nearest three decimal places.
- A psychologist determined that the number of sessions required to obtain the trust of a new patient is either 1, 2, or 3. Let x be a random variable indicating the number of sessions re- quired to gain the patient's trust. The following probability function has been proposed. f(x) = for x = 1, 2, or 3 6. Is this probability function valid? Explain. b. What is the probability that it takes exactly two sessions to gain the patient's trust? с. What is the probability that it takes at least two sessions to gain the patient's trust?Find the probability P(Ec) if P(E)=0.17.Find the probability functions for the following: a. X + Y b. XY c. X/Y
