Statistics - MathematicalStatistics - quiz1

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

3.5 2.5 4.5 5.5

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

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

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

n/2 (n-1)/2 n (n+1)/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, $\mu=1$

0 -1 2 1

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

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

Question 7: What does the Central Limit Theorem state?

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

Question 8: What is the formula for standard deviation?

variance/2 mean/2 mean² √(variance)

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

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

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

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

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