please explain this qustion. Let X ∼N(1,4) and g(t) = P(X > t), −∞< t <∞....
please explain this qustion. Let X ∼N(1,4) and g(t) = P(X > t), −∞< t <∞. (a) Find the value t that minimizes g(t+4)−g(t) and justify your answer. (b) Redo (a) for X ∼N(1,σ2). Does your answer depend on σ? Explain why.
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please explain this qustion. Let X ∼N(1,4) and g(t) = P(X >
t), −∞< t <∞....
4. Suppose that x = (x1, r.) is a sample from a N(μ, σ2) distribution where μ E R, σ2 > 0 are unk...
Please explain very carefully!
4. Suppose that x = (x1, r.) is a sample from a N(μ, σ2) distribution where μ E R, σ2 > 0 are unknown. (a) (5 marks) Let μ+σ~p denote the p-th quantile of the N(μ, σ*) distribution. What does this mean? (b) (10 marks) Determine a UMVU estimate of,1+ ơZp and justify your answer.
4. Suppose that x = (x1, r.) is a sample from a N(μ, σ2) distribution where μ E R, σ2 >...
3. Let Xi, , Xn be i.i.d. Lognormal(μ, σ2) (a) Suppose σ-1, prove that S-X(n)/X(i) is an ancillar...
3. Let Xi, , Xn be i.i.d. Lognormal(μ, σ2) (a) Suppose σ-1, prove that S-X(n)/X(i) is an ancillary statistics. (b) Suppose p 0, prove T-X(n) is a sufficient and complete statistics (c) Find a minimal sufficient statistics.
3. Let Xi, , Xn be i.i.d. Lognormal(μ, σ2) (a) Suppose σ-1, prove that S-X(n)/X(i) is an ancillary statistics. (b) Suppose p 0, prove T-X(n) is a sufficient and complete statistics (c) Find a minimal sufficient statistics.
1. Let T : P (R) Pn+1(R) be defined: T(p()) = (x + 1)p(x + 2)...
1. Let T : P (R) Pn+1(R) be defined: T(p()) = (x + 1)p(x + 2) (a) (2 marks) Show that T is a linear transformation. (b) (3 marks) Is T one-to-one? Describe ker(T). What is the rank of T? (c) (8 marks) Find a matrix representation for T with respect to the standard bases {1, 2, ..., 2"} for Pn and {1, 2, ..., xn+1} for Pn+1 if n = 4. (d) (5 marks) Let D : Pn+1(R) +...
please explain in detail 4 -11 23 4 Graph of f Let f be a continuous function defined on the closed interval -1Sxs4. The graph of f, consisting of three line segments, is shown above. Let g be...
please explain in detail
4 -11 23 4 Graph of f Let f be a continuous function defined on the closed interval -1Sxs4. The graph of f, consisting of three line segments, is shown above. Let g be the function defined by g(x) = 5 +1.f(t) dt for-1 $154. (A) Find g(4). (B) On what intervals is gincreasing? Justify your answer. (C) On the closed interval 1 s xs 4, find the absolute minimum value of g and find the...
) 6. Let x be the binomial random variable with n = 10 and p =...
) 6. Let x be the binomial random variable with n = 10 and p = .9 (2) a. Find P(x = 8) (5) b. Create a cumulative probability table for the distribution. (2) c. Find P( x is less than or equal to 7) (2) d. Find P(x is greater than 7) e. Find the mean, μ. (1) f. Find the standard deviation, σ. (1) g. Find the variance. ...
1. Let T : Pn(R) + Pn+1(R) be defined: T(P(x)) = (x + 1)p(x + 2)...
1. Let T : Pn(R) + Pn+1(R) be defined: T(P(x)) = (x + 1)p(x + 2) bases {1, X, ..., (a) (2 marks) Show that T is a linear transformation. (b) (3 marks) Is T one-to-one? Describe ker(T). What is the rank of T? (c) (8 marks) Find a matrix representation for T with respect to the standard xn} for Pn and {1, 2, ..., xn+1} for Pn+1 if n = 4. (d) (5 marks) Let D : Pn+1(R) +...
5. Partitions For each n e Z, let T={(x, y) + R n<I- g < n+1}....
5. Partitions For each n e Z, let T={(x, y) + R n<I- g < n+1}. Is T = {T, n € Z} a partition of R?? Justify your answer using the definition.
1. Let T: Pn(R) + Pn+1(R) be defined: T(P(x)) = (x + 1)p(x + 2) (c)...
1. Let T: Pn(R) + Pn+1(R) be defined: T(P(x)) = (x + 1)p(x + 2) (c) (8 marks) Find a matrix representation for T with respect to the standard bases {1, 2, ...,2"} for Pn and {1, 2, ...,xN+1} for Pn+1 if n = 4. (d) (5 marks) Let D : Pn+1(R) + Pn(R) be the derivative operator. What is the rank of DoT? Justify your answer. Describe ker(DoT). Is DoT one-to-one? (e) (5 marks) What is the rank of...
6. Let T: P2P be the linear operator defined as T(p(x)) = P(5x), and let B...
6. Let T: P2P be the linear operator defined as T(p(x)) = P(5x), and let B = {1,x,x?} be the standard basis for P2 a.) (5 points) Find [T), the matrix for T relative to B. b.) (4 points) Let p(x) = x + 6x2 Determine [p(x)]s, then find T(p(x)) using [T]g from part a. c.) (1 point) Check your answer to part b by evaluating T(x + 6x) directly
4. Let X be a random variable with distribution P( x =-2) = 1 /2 P(X...
4. Let X be a random variable with distribution P( x =-2) = 1 /2 P(X = 3) = 1/3, P(X = a) = 1/6· , Find the value a that minimizes the variance of X t Dato vorrorelineg he nmher of onidente on n proceineg Cor tho ware 9000 9001 010 rn
Please explain very carefully!
4. Suppose that x = (x1, r.) is a sample from a N(μ, σ2) distribution where μ E R, σ2 > 0 are unknown. (a) (5 marks) Let μ+σ~p denote the p-th quantile of the N(μ, σ*) distribution. What does this mean? (b) (10 marks) Determine a UMVU estimate of,1+ ơZp and justify your answer.
4. Suppose that x = (x1, r.) is a sample from a N(μ, σ2) distribution where μ E R, σ2 >...
3. Let Xi, , Xn be i.i.d. Lognormal(μ, σ2) (a) Suppose σ-1, prove that S-X(n)/X(i) is an ancillary statistics. (b) Suppose p 0, prove T-X(n) is a sufficient and complete statistics (c) Find a minimal sufficient statistics.
3. Let Xi, , Xn be i.i.d. Lognormal(μ, σ2) (a) Suppose σ-1, prove that S-X(n)/X(i) is an ancillary statistics. (b) Suppose p 0, prove T-X(n) is a sufficient and complete statistics (c) Find a minimal sufficient statistics.
1. Let T : P (R) Pn+1(R) be defined: T(p()) = (x + 1)p(x + 2) (a) (2 marks) Show that T is a linear transformation. (b) (3 marks) Is T one-to-one? Describe ker(T). What is the rank of T? (c) (8 marks) Find a matrix representation for T with respect to the standard bases {1, 2, ..., 2"} for Pn and {1, 2, ..., xn+1} for Pn+1 if n = 4. (d) (5 marks) Let D : Pn+1(R) +...
please explain in detail
4 -11 23 4 Graph of f Let f be a continuous function defined on the closed interval -1Sxs4. The graph of f, consisting of three line segments, is shown above. Let g be the function defined by g(x) = 5 +1.f(t) dt for-1 $154. (A) Find g(4). (B) On what intervals is gincreasing? Justify your answer. (C) On the closed interval 1 s xs 4, find the absolute minimum value of g and find the...
1. Let T : Pn(R) + Pn+1(R) be defined: T(P(x)) = (x + 1)p(x + 2) bases {1, X, ..., (a) (2 marks) Show that T is a linear transformation. (b) (3 marks) Is T one-to-one? Describe ker(T). What is the rank of T? (c) (8 marks) Find a matrix representation for T with respect to the standard xn} for Pn and {1, 2, ..., xn+1} for Pn+1 if n = 4. (d) (5 marks) Let D : Pn+1(R) +...
5. Partitions For each n e Z, let T={(x, y) + R n<I- g < n+1}. Is T = {T, n € Z} a partition of R?? Justify your answer using the definition.
1. Let T: Pn(R) + Pn+1(R) be defined: T(P(x)) = (x + 1)p(x + 2) (c) (8 marks) Find a matrix representation for T with respect to the standard bases {1, 2, ...,2"} for Pn and {1, 2, ...,xN+1} for Pn+1 if n = 4. (d) (5 marks) Let D : Pn+1(R) + Pn(R) be the derivative operator. What is the rank of DoT? Justify your answer. Describe ker(DoT). Is DoT one-to-one? (e) (5 marks) What is the rank of...
6. Let T: P2P be the linear operator defined as T(p(x)) = P(5x), and let B = {1,x,x?} be the standard basis for P2 a.) (5 points) Find [T), the matrix for T relative to B. b.) (4 points) Let p(x) = x + 6x2 Determine [p(x)]s, then find T(p(x)) using [T]g from part a. c.) (1 point) Check your answer to part b by evaluating T(x + 6x) directly
4. Let X be a random variable with distribution P( x =-2) = 1 /2 P(X = 3) = 1/3, P(X = a) = 1/6· , Find the value a that minimizes the variance of X t Dato vorrorelineg he nmher of onidente on n proceineg Cor tho ware 9000 9001 010 rn
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