Understanding Sums and Differences of Random Variables

What is the expected value of a random variable?

• The range of the random variable

• The median of the random variable

• The mean of the random variable

• The mode of the random variable

How is the variance of a random variable defined?

• The expected value of the squared differences from the mean

• The square root of the expected value

• The average of the random variable

• The sum of the squared differences from the mean

What is the expected value of the sum of two independent random variables?

• The average of their expected values

• The difference of their expected values

• The sum of their expected values

• The product of their expected values

How do you calculate the expected value of the difference between two independent random variables?

• Subtract the expected value of the second from the first

• Add the expected values

• Multiply the expected values

• Divide the expected values

What is the variance of the sum of two independent random variables?

• The average of their variances

• The difference of their variances

• The sum of their variances

• The product of their variances

Why is the variance of the sum of two independent random variables the sum of their variances?

• Because they are unrelated

• Because they are identical

• Because they are dependent

• Because they are inversely related

What is the variance of the difference between two independent random variables?

• The product of their variances

• The average of their variances

• The difference of their variances

• The sum of their variances

How does the variance of a negative random variable compare to the variance of the positive version?

• It is double the variance of the positive version

• It is half the variance of the positive version

• It is the same as the variance of the positive version

• It is zero

What is a key takeaway about the mean of differences of random variables?

• It is the sum of their means

• It is the difference of their means

• It is the product of their means

• It is the average of their means

What is a key takeaway about the variance of differences of random variables?

• It is the sum of their variances

• It is the difference of their variances

• It is the product of their variances

• It is the average of their variances