1. What is a random variable? Give an example. 2. Create an ordinary and cumulative probability distribution table and probability distribution visualization for an experiment involving the random variable \"the number of heads with 3 coin flips\" 3. What is the expected value of the random variable defined in question 2? Show your work. 4. What is the standard deviation of the random variable defined in question 2? Show your work. 5. What is the expected proportion of heads in 3 coin flips? 6. Using the binomial distribution formula, calculate the probability of getting exactly 5 heads in 12 coin flips. Show your work. 7. Using the binomial distribution formula, calculate the probability of getting exactly 2 \"sixes\" when you roll a die 7 times. Show your work. A technology start-up company has had 5 different CEOs since it was founded. The tenures of these CEOs - the number of months that they held the position - are given in the table below. These 5 CEOs are the population you are interested in. CE O 1 2 3 4 5 Tenure (in months) 12 14 6 19 12 1. You randomly select a sample of 2 CEOs from the population. The sample you get is (CEO3, CEO4). Based on this sample, what is your point estimate of the population mean of tenure? 2. Calculate the sampling error of the point estimate you found in question 1. Are you underestimating or overestimating the population mean? 3. Suppose that you randomly sample 2 CEOs without replacement. In the table below, list all possible samples you could select and the value of the sample mean of tenure ( x ) in each sample. Sample x 4. Under simple random sampling, what is the probability of each sample you wrote down in question 3? 5. For each CEO, calculate the probability that he/she is selected into a sample. Comment on your answer. 6. Use your answers to questions 3 and 4 to write down the probability distribution of the sample mean x (i.e. a table with possible outcomes and associated probabilities). 7. Calculate the expected value of mean of tenure? x . How does your answer compare to the population 8. Suppose that you sampled 2 CEOs with replacement instead. How many different samples are possible, and what is the probability of each sample occurring? A technology start-up company has had 5 different CEOs since it was founded. The tenures of these CEOs - the number of months that they held the position - are given in the table below. These 5 CEOs are the population you are interested in. CE O 1 2 3 4 5 Tenure (in months) 12 14 6 19 12 1. You randomly select a sample of 2 CEOs from the population. The sample you get is (CEO3, CEO4). Based on this sample, what is your point estimate of the population mean of tenure? 2. Calculate the sampling error of the point estimate you found in question 1. Are you underestimating or overestimating the population mean? 3. Suppose that you randomly sample 2 CEOs without replacement. In the table below, list all possible samples you could select and the value of the sample mean of tenure ( x ) in each sample. Sample x 4. Under simple random sampling, what is the probability of each sample you wrote down in question 3? 5. For each CEO, calculate the probability that he/she is selected into a sample. Comment on your answer. 6. Use your answers to questions 3 and 4 to write down the probability distribution of the sample mean x (i.e. a table with possible outcomes and associated probabilities). 7. Calculate the expected value of mean of tenure? x . How does your answer compare to the population 8. Suppose that you sampled 2 CEOs with replacement instead. How many different samples are possible, and what is the probability of each sample occurring