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Let E, F, G be events in a sample space S. We say that two events E and F are conditionally independent given G if P (E ∩ F |G) = P (E|G)P (F |G). (a) If E and F are independent events, are E and F necessarily conditionally independent given G? Provide a proof or counterexample to justify your answer. (b) If E and F are conditionally independent given G, is it necessarily true that E and F are independent events? Again, provide a proof or counterexample to justify your answer. Suppose that a die is rolled twice. Let X be the random variable "the minimum value that appears in the two rolls". Let Y be the random variable "the value of the first roll minus the value of the second roll". (a) What values can X take on? What values can Y take on? (b) Compute the probability mass function for X. Compute the cumulative distribution function for X. Graph these functions. (c) Compute the probability mass function, and the cumulative distribution function for Y . Graph these functions.
Discuss the level of measurement, assumptions that can be made, statistics that can be calculated from these data, and the general quality of the data
Research paper examines determine the impact of social media use on student learning.
condence interval fornbspmu when sigma is knownsuppose n 9 people are selected at random from a large population.
1. in this exercise we will be building regression models for predicting house prices. we will be using data collected
Analyze whether gender differences exist in the size of pay-raise and whether or not these differences are attributable to the size of the university.
How should they use the information from the labs?
The researchers used the available survey data and summarised the nature of the car accidents and if a mobile phone was being used by the driver either during (or immediately before) the accident
Prepare a single summary table that shows average and standard deviation of current salary for males and females according to their Position within the company.
Calculate the sample size needed given these factors
The company wants to perform a hypothesis testing. Which of the following are the right hypotheses and what is the α-risk associated with the x' chart?
List and explain the variables you would collect in this study. There must be a minimum of three variables and two must meet the assumptions for a correlational analysis.
ANOVA and Factorial Designs
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