Question

Part I: Determine whether each of the following statements is TRUE or FALSE, and write a short explanation for your answer

1. The mean and median are always equal to each other and can never be different.
2. The median and mode must always be equal and can never be different.
3. The expected value of a random variable is a weighted average of outcomes, where each outcome is weighted by its probability of occurrence.
4. Regressions are used to estimate the relationship between a dependent variable and only one independent variable.
5. In a linear regression, we are usually interested in estimating the slope and y-intercept.
6. Only the dependent variable in a regression can take the form of a dummy variable.
7. One way to estimate quadratic relationships is by including dummy variables in the regression.
8. If the correlation coefficient between x and y is -1, it means that those variables are perfectly negatively correlated.
9. The higher the variance of a given random variable, the closer the outcomes are relative to the mean.
10. If the cumulative distribution function is greater than 1, we know the variable is close to its maximum value.

Answer 1

1. False. It is equal only under normal distribution
2. False. It is equal only under normal distribution
3. True. It is the sum product of each possible outcome with the probability of the outcome occurring
4. False. It is used to estimate relationship with one and many independent variable
5. True. As slope tells about the change in Y for a change in X, intercept tells about the average value
6. True. It can take values of 1 or 0
7. True
8. True, means variables inversely related like demand and price
9. False. More the variance more is the spread from mean
10. False. The maximum value is 1