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Note: The gamma function satisfies many useful relationships, in particular,
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3. If X ~ Nga ?2), what is the median of X? Justify your answer (this...
If X ~ N(?, ?2), what is the median of X? Justify your answer (this does...
If X ~ N(?, ?2), what is the median of X? Justify your answer (this does not have to be a proof). If Y ~ Gamma (?, ?), show that (a) E(Y)-??. (c) V(Y)???2
8 pts Question 3 Consider the function f(x,y, 2)(x 1)3(y2)3 ( 1)2(y2)2(z 3)2 (a) Compute the...
8 pts Question 3 Consider the function f(x,y, 2)(x 1)3(y2)3 ( 1)2(y2)2(z 3)2 (a) Compute the increment Af if (r,y, z) changes from (1,2,3 (b) Compute the differential df for the corresponding change in position. What does (2,3,4) to this say about the point (1, 2,3)? ( 13y2)3 ( 1)2(y 2)2(z 3)2 with C (c) Consider the contour C = a constant. Use implicit differentiation to compute dz/Ox. Your answer should be a function of z. (d) Find the unit...
1. Answer the following questions. Justify your answers. (a) (3 marks) For what values of x...
1. Answer the following questions. Justify your answers. (a) (3
marks) For what values of x does the series 1 + 22x 2 + 24x 4 + 26x
6 · · · + 22nx 2n + · · · converge? (b) (9 marks) Is the following
series absolutely convergent, conditionally convergent or
divergent? i. X∞ n=1 2 √ n − 2 √ n + 1 ii. X∞ n=1 arctan(n) n2 + 1
iii. X∞ k=1 (−1)k k
1. Answer the...
8. (10 Pts) Answer by True / False and justify your answer. (a) Let A be...
8. (10 Pts) Answer by True / False and justify your answer. (a) Let A be a 2 × 2 matrix such that(A2-Nthen, if A ±1 A--. (b) If C is a skew-symmetric matrix of odd order n, then |C-0 (c) If A is a square matrix, and the linear transformation L(z) Az is one-to-one, then the linear transformation x ? At is also one-toone. z), ? O (z, y, z) = (az, ay, 0), then V is not a...
Problem 1. Consider the two data collections (x,..-, X) and (y,. ya). The median difference statistic...
Problem 1. Consider the two data collections (x,..-, X) and (y,. ya). The median difference statistic is the median of the (v-x) differences for the mn possible (x, y.) pairings, i= 1, ..., mandj = 1, . . ., n. Construct two specific data collections (x,. Xm) and (y,. .. V) that demonstrate that the median difference statistic is not equal to the difference in the separate medians for the two collections Problem 2. A Venn diagram is a graphical...
Answer all 3 and I will positively rate your answer 1. F(x, y, z) = (x,y2,...
Answer all 3 and I will positively rate your answer
1. F(x, y, z) = (x,y2, z3), S is a surface bounded by the cylinder x2 + y2 = 4,2 = 0 and z = 1. Evaluate the outward flux Sf. Nds using the Divergence Theorem. S 2. F(x, y, z) = (2x3, 2y3, 3z2), S is a surface bounded by the cylinder x2 + y2 = 4, z = 0 and z = 1. Evaluate the outward flux Sf....
(b) (5 points) Are X and Y independent? Justify your answer. (c) (5 points) Identify the...
(b) (5 points) Are X and Y independent? Justify your answer.
(c) (5 points) Identify the random variable expressed as the
conditional expectation of Y given X, i.e., E[Y |X].
6. (15 points) Consider two independent Bernoulli r.v., U and V, both with probability of success 1/2. Let X = U+V and Y = |U - VI. (a) (5 points) Calculate the covariance of X and Y , oxy.
Please justify your answers : Which of the following sets are compact: i. {(z, y)E R...
Please justify your answers :
Which of the following sets are compact: i. {(z, y)E R 2 - 2y2 < 1} ii. {(, y) R22 < 2x2 + y2 < 4} ii. {(esin(ar), e cos(x)) R2: x 2 0}U {(x,0) E R2 : 0 iv. {(esin(0), e cos (0)) R2 x 2 0, 00 2r} x< 1}
1. Consider the three reaction energy diagrams below. Make sure you can justify your answer for...
1. Consider the three reaction energy diagrams below. Make sure you can justify your answer for the purposes of Exam 3 – simply guessing on this multiple choice question will NOT help you when you're asked to explain your reasoning on the exam! energy energy energy reaction coordinate reaction coordinate reaction coordinate i) Which forward reaction do you expect to proceed fastest, assuming the same energy scale for each? ii) Which reaction do you expect to be the most favorable...
1. Consider the three reaction energy diagrams below. Make sure you can justify your answer for...
1. Consider the three reaction energy diagrams below. Make sure you can justify your answer for the purposes of Exam 3 - simply guessing on this multiple choice question will NOT help you when you're asked to explain your reasoning on the exam! energy- energy- reaction coordinate reaction coordinate reaction coordinate i) Which forward reaction do you expect to proceed fastest, assuming the same energy scale for each? ii) Which reaction do you expect to be the most favorable in...
If X ~ N(?, ?2), what is the median of X? Justify your answer (this does not have to be a proof). If Y ~ Gamma (?, ?), show that (a) E(Y)-??. (c) V(Y)???2
8 pts Question 3 Consider the function f(x,y, 2)(x 1)3(y2)3 ( 1)2(y2)2(z 3)2 (a) Compute the increment Af if (r,y, z) changes from (1,2,3 (b) Compute the differential df for the corresponding change in position. What does (2,3,4) to this say about the point (1, 2,3)? ( 13y2)3 ( 1)2(y 2)2(z 3)2 with C (c) Consider the contour C = a constant. Use implicit differentiation to compute dz/Ox. Your answer should be a function of z. (d) Find the unit...
1. Answer the following questions. Justify your answers. (a) (3
marks) For what values of x does the series 1 + 22x 2 + 24x 4 + 26x
6 · · · + 22nx 2n + · · · converge? (b) (9 marks) Is the following
series absolutely convergent, conditionally convergent or
divergent? i. X∞ n=1 2 √ n − 2 √ n + 1 ii. X∞ n=1 arctan(n) n2 + 1
iii. X∞ k=1 (−1)k k
1. Answer the...
8. (10 Pts) Answer by True / False and justify your answer. (a) Let A be a 2 × 2 matrix such that(A2-Nthen, if A ±1 A--. (b) If C is a skew-symmetric matrix of odd order n, then |C-0 (c) If A is a square matrix, and the linear transformation L(z) Az is one-to-one, then the linear transformation x ? At is also one-toone. z), ? O (z, y, z) = (az, ay, 0), then V is not a...
Problem 1. Consider the two data collections (x,..-, X) and (y,. ya). The median difference statistic is the median of the (v-x) differences for the mn possible (x, y.) pairings, i= 1, ..., mandj = 1, . . ., n. Construct two specific data collections (x,. Xm) and (y,. .. V) that demonstrate that the median difference statistic is not equal to the difference in the separate medians for the two collections Problem 2. A Venn diagram is a graphical...
Answer all 3 and I will positively rate your answer
1. F(x, y, z) = (x,y2, z3), S is a surface bounded by the cylinder x2 + y2 = 4,2 = 0 and z = 1. Evaluate the outward flux Sf. Nds using the Divergence Theorem. S 2. F(x, y, z) = (2x3, 2y3, 3z2), S is a surface bounded by the cylinder x2 + y2 = 4, z = 0 and z = 1. Evaluate the outward flux Sf....
(b) (5 points) Are X and Y independent? Justify your answer.
(c) (5 points) Identify the random variable expressed as the
conditional expectation of Y given X, i.e., E[Y |X].
6. (15 points) Consider two independent Bernoulli r.v., U and V, both with probability of success 1/2. Let X = U+V and Y = |U - VI. (a) (5 points) Calculate the covariance of X and Y , oxy.
Please justify your answers :
Which of the following sets are compact: i. {(z, y)E R 2 - 2y2 < 1} ii. {(, y) R22 < 2x2 + y2 < 4} ii. {(esin(ar), e cos(x)) R2: x 2 0}U {(x,0) E R2 : 0 iv. {(esin(0), e cos (0)) R2 x 2 0, 00 2r} x< 1}
1. Consider the three reaction energy diagrams below. Make sure you can justify your answer for the purposes of Exam 3 – simply guessing on this multiple choice question will NOT help you when you're asked to explain your reasoning on the exam! energy energy energy reaction coordinate reaction coordinate reaction coordinate i) Which forward reaction do you expect to proceed fastest, assuming the same energy scale for each? ii) Which reaction do you expect to be the most favorable...
1. Consider the three reaction energy diagrams below. Make sure you can justify your answer for the purposes of Exam 3 - simply guessing on this multiple choice question will NOT help you when you're asked to explain your reasoning on the exam! energy- energy- reaction coordinate reaction coordinate reaction coordinate i) Which forward reaction do you expect to proceed fastest, assuming the same energy scale for each? ii) Which reaction do you expect to be the most favorable in...
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