6.2 - Mean and SD of Combinations and Transformations

Front

What is the mean of a random variable?

Back

The mean of a random variable is the average value it takes, calculated as the sum of all possible values multiplied by their probabilities.

Front

What is standard deviation (SD)?

Back

Standard deviation is a measure of the amount of variation or dispersion in a set of values. A low SD indicates that the values tend to be close to the mean, while a high SD indicates that the values are spread out over a wider range.

Front

What is a transformation in statistics?

Back

A transformation is a mathematical operation applied to a random variable that changes its scale or location, such as converting feet to inches.

Front

What is a combination in statistics?

Back

A combination refers to the addition or aggregation of two or more random variables, such as summing the heights of two individuals.

Front

How do you convert feet to inches?

Back

To convert feet to inches, multiply the number of feet by 12, since there are 12 inches in a foot.

Front

How do you convert inches to centimeters?

Back

To convert inches to centimeters, multiply the number of inches by 2.54, since there are 2.54 centimeters in an inch.

Front

If a random variable X has a mean of 10 and a standard deviation of 2, what is the mean of 2X?

Back

The mean of 2X is 2 * 10 = 20.

Front

If a random variable Y has a mean of 5 and a standard deviation of 1, what is the standard deviation of 3Y?

Back

The standard deviation of 3Y is 3 * 1 = 3.

Front

What is the formula for the standard deviation of a transformed variable?

Back

If Y = aX + b, where a and b are constants, then the standard deviation of Y is |a| * SD(X).

Front

What is the mean of a sum of two independent random variables?

Back

The mean of the sum of two independent random variables is the sum of their means: E(X + Y) = E(X) + E(Y).