Introduction to Probability · free preview
LOTUS, Variance and Standard Deviation
Computing E of g(X) directly from the distribution of X, measuring spread by variance and standard deviation, and the algebra of variances.
1. LOTUS
LOTUS
2. Variance
Variance
3. Variance of sums and independence
Variance of sums and independence
4. LOTUS applied
X is a fair die roll. Which expression gives the expected payout of a game paying the absolute difference between X and 3?
5. Variance of a sum
X and Y are independent with Var(X) = 4 and Var(Y) = 9. What is Var(X + Y)?
6. Variance shortcut
E(X) = 2 and E(X squared) = 7. What is Var(X)? Enter an integer.
7. Binomial variance
X is Binomial(20, 0.3). What is Var(X)? Enter a decimal like 4.2.
8. Scaling variance
Temperatures in Celsius have variance 25. Converted to Fahrenheit, F = 1.8 C + 32, what is the variance of F? Enter like 81.
9. In your own words
In your own words, state the most important definition, theorem or method of this lesson and explain what it says.
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