Statistics - MathematicalStatistics - quiz1

Question 1: What is the Expectation of a 6-sided die roll?

2.5 4.5 3.5 5.5

Question 2: What is the Variance of a 6-sided die roll?

15/12 35/12 25/12 5/12

Question 3: What is the expectation of a n-sided die roll?

(n+1)/2 (n-1)/2 n n/2

Question 4: What is the variance of a n-sided die roll?

(n^2-1)/6 (n^2+1)/6 (n^2+1)/12 (n^2-1)/12

Question 5: What is the expectation of a normal function with parameters var=0, $\mu=1$

1 0 -1 2

Question 6: What is the covariance of two independent variables?

1 0 E[XY] var(X)*var(Y)

Question 7: What does the Central Limit Theorem state?

All distributions are normal Standard deviation is always 1 The mean of sample means equals the population mean Variance equals mean

Question 8: What is the formula for standard deviation?

√(variance) mean/2 variance/2 mean²

Question 9: What is P(A|B)?

P(A)*P(B) P(A∩B)/P(B) P(B)/P(A) P(A)+P(B)

Question 10: What is the expected value of a uniform distribution on [a,b]?

b-a a (a+b)/2 (b-a)/2

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