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Question 4: Summation Notation Practice Zi 2.0 -2.0 3.0 3.0 (i) Compute Σ㈡zī (ii) Compute Σ41...
3. Let Xi, . . . , Xn be iid randoln variables with mean μ and...
3. Let Xi, . . . , Xn be iid randoln variables with mean μ and variance σ2. Let, X denote the sample mean and V-Σ, (X,-X)2. (a) Derive the expected values of X and V. (b) Further suppose that Xi,-.,X, are normally distributed. Let Anxn ((a)) an orthogonal matrix whose first rOw 1S be , ..*) and iet Y = AX, where Y (Yİ, ,%), ard X-(XI, , X.), are (column) vectors. (It is not necessary to know aij...
I don't understand a iii and b ii, What's the procedure of deriving the limit distribution? Thanks. 6. Extreme...
I don't understand a iii and b ii, What's the procedure of
deriving the limit distribution? Thanks.
6. Extreme values are of central importance in risk management and the following two questions provide the fundamental tool used in the extreme value theory. (a) Let Xi,... , Xn be independent identically distributed (i. i. d.) exp (1) random variables and define max(Xi,..., Xn) (i) Find the cumulative distribution of Zn (ii) Calculate the cumulative distribution of Vn -Zn - Inn (iii)...
9. Consider the following hidden Markov model (HMM) (This is the same HMM as in the previous HMM problem): ·X=(x, ,...
9. Consider the following hidden Markov model (HMM) (This is the same HMM as in the previous HMM problem): ·X=(x, ,x,Je {0,1)、[i.e., X is a binary sequence of length n] and Y-(Y Rt [i.e. Y is a sequence of n real numbers.) ·X1~" Bernoulli(1/2) ,%) E Ip is the switching probability; when p is small the Markov chain likes to stay in the same state] . conditioned on X, the random variables Yı , . . . , y, are...
3. Let Xi, . . . , Xn be iid randoln variables with mean μ and variance σ2. Let, X denote the sample mean and V-Σ, (X,-X)2. (a) Derive the expected values of X and V. (b) Further suppose that Xi,-.,X, are normally distributed. Let Anxn ((a)) an orthogonal matrix whose first rOw 1S be , ..*) and iet Y = AX, where Y (Yİ, ,%), ard X-(XI, , X.), are (column) vectors. (It is not necessary to know aij...
I don't understand a iii and b ii, What's the procedure of
deriving the limit distribution? Thanks.
6. Extreme values are of central importance in risk management and the following two questions provide the fundamental tool used in the extreme value theory. (a) Let Xi,... , Xn be independent identically distributed (i. i. d.) exp (1) random variables and define max(Xi,..., Xn) (i) Find the cumulative distribution of Zn (ii) Calculate the cumulative distribution of Vn -Zn - Inn (iii)...
9. Consider the following hidden Markov model (HMM) (This is the same HMM as in the previous HMM problem): ·X=(x, ,x,Je {0,1)、[i.e., X is a binary sequence of length n] and Y-(Y Rt [i.e. Y is a sequence of n real numbers.) ·X1~" Bernoulli(1/2) ,%) E Ip is the switching probability; when p is small the Markov chain likes to stay in the same state] . conditioned on X, the random variables Yı , . . . , y, are...
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