All Flashcards
Explain the effect of adding a constant to a random variable.
Shifts the mean by the constant; standard deviation remains unchanged.
Explain the effect of multiplying a random variable by a constant.
Multiplies both the mean and the standard deviation by the constant (absolute value for SD).
Explain how to find the mean of the sum of two random variables.
The mean of the sum is the sum of the means: E(X + Y) = E(X) + E(Y).
Explain how to find the mean of the difference of two random variables.
The mean of the difference is the difference of the means: E(X - Y) = E(X) - E(Y).
Explain how to find the standard deviation of the sum or difference of two independent random variables.
First, find the variance of the sum/difference by adding the variances. Then, take the square root to find the standard deviation.
Why do we use variances when combining random variables?
Variances represent the 'energy' of the random variables, which add up when combining them. Standard deviations don't add directly.
If Y = X + c, what is E(Y)?
E(Y) = E(X) + c
If Y = X + c, what is SD(Y)?
SD(Y) = SD(X)
If Y = c * X, what is E(Y)?
E(Y) = c * E(X)
If Y = c * X, what is SD(Y)?
SD(Y) = |c| * SD(X)
If S = X + Y, what is E(S)?
E(S) = E(X) + E(Y)
If D = X - Y, what is E(D)?
E(D) = E(X) - E(Y)
If S = X + Y, what is Var(S)?
Var(S) = Var(X) + Var(Y)
If D = X - Y, what is Var(D)?
Var(D) = Var(X) + Var(Y)
If S = X + Y, what is SD(S)?
SD(S) =
If D = X - Y, what is SD(D)?
SD(D) =
What are the differences between adding a constant and multiplying by a constant in transforming a random variable?
Adding: Shifts the center, no change to spread. | Multiplying: Changes both the center and the spread.
What are the differences between the effects on variance and standard deviation when combining random variables?
Variance: Variances are added together. | Standard Deviation: Standard Deviation is the square root of the added variances.
What are the differences between calculating the mean of a sum versus the standard deviation of a sum of random variables?
Mean of Sum: Add the means directly. | Standard Deviation of Sum: Add the variances, then take the square root.
What are the differences between calculating the mean of a difference versus the standard deviation of a difference of random variables?
Mean of Difference: Subtract the means directly. | Standard Deviation of Difference: Add the variances, then take the square root.
What are the differences between standard deviation and variance?
Standard deviation: Measure of dispersion expressed in the same units as the data. | Variance: Measure of dispersion expressed in squared units.