1. Let W be the collection of polynomials, p(x), for which p'(5)=0 (the derivative of the...

1. Let W be the collection of polynomials, p(x), for which p'(5)=0 (the derivative of the polynomial when x = 5 is 0).

State two polynomials that would belong to this set, W.
State one polynomial that does not belong to this set.
Is W a subspace of the vector space containing all polynomial functions? That is, is this subset of polynomials closed under addition and scalar multiplication, and does it contain a zero vector? Justify your answer. (You do not have to give a detailed proof, but you should thoroughly explain your thought process using the theorems in section 4.1.)

2. If the definition of the subset W is changed to the collection of polynomials, p(x), for which p'(5)=1, does that change your verdict as to whether W is a subspace? Explain your answer

Expert Solution

Colby Messinger answered 1 week ago

Let W be the set of P4 consisting if all polynomials satisfying the conditions p(-2)=0. a.)...

Let W be the set of P4 consisting if all polynomials satisfying the conditions p(-2)=0. a.) prove that W is a subspace of P4 by checking all 3 conditions in the definition of subspace. b.) Find a basis for W. Prove that your basis is actually a basis for W by showing it is both linearly independent and spans W c.) what is the dim(W)

Let f(x) = −3+(3x2 −x+1) ln(2√x−5) (a) Find the derivative of f. (b) Using the derivative...

Let f(x) = −3+(3x2 −x+1) ln(2√x−5) (a) Find the derivative of f. (b) Using the derivative and linear approximation, estimate f(9.1).

Let X and Y be random variables. Suppose P(X = 0, Y = 0) = .1,...

Let X and Y be random variables. Suppose P(X = 0, Y = 0) = .1, P(X = 1, Y = 0) = .3, P(X = 2, Y = 0) = .2 P(X = 0, Y = 1) = .2, P(X = 1, Y = 1) = .2, P(X = 2, Y = 1) = 0. a. Determine E(X) and E(Y ). b. Find Cov(X, Y ) c. Find Cov(2X + 3Y, Y ).

1. Let X be random variable with density p(x) = x/2 for 0 < x<...

1. Let X be random variable with density p(x) = x/2 for 0 < x < 2 and 0 otherwise. Let Y = X^2−2. a) Compute the CDF and pdf of Y. b) Compute P(Y >0 | X ≤ 1.8).

2. Let X ~ Geometric (p) where 0 < p <1 a. Show explicitly that this...

2. Let X ~ Geometric (p) where 0 < p <1 a. Show explicitly that this family is “very regular,” that is, that R0,R1,R2,R3,R4 hold. R 0 - different parameter values have different functions. R 1 - parameter space does not contain its own endpoints. R 2. - the set of points x where f (x, p) is not zero and should not depend on p. R 3. One derivative can be found with respect to p. R 4. Two...

Let X ~ Geometric (p) where 0 < p <1 a) Show explicitly that this family...

Let X ~ Geometric (p) where 0 < p <1 a) Show explicitly that this family is “very regular,” that is, that R0,R1,R2,R3,R4 hold. R 0 - different parameter values have different functions. R 1 - parameter space does not contain its own endpoints. R 2. - the set of points x where f (x, p) is not zero and should not depend on p. R 3. One derivative can be found with respect to p. R 4. Two derivatives...

Question 1 Let f be a function for which the first derivative is f ' (x)...

Question 1 Let f be a function for which the first derivative is f ' (x) = 2x 2 - 5 / x2 for x > 0, f(1) = 7 and f(5) = 11. Show work for all question. a). Show that f satisfies the hypotheses of the Mean Value Theorem on [1, 5] b)Find the value(s) of c on (1, 5) that satisfyies the conclusion of the Mean Value Theorem. Question 2 Let f(x) = x 3 − 3x...

Let X~Geometric(p), with parameter p unknown, 0<p<1. a) Find I(p), the Fisher Information in X about...

Let X~Geometric(p), with parameter p unknown, 0<p<1. a) Find I(p), the Fisher Information in X about p. b) Suppose that pˆ is some unbiased estimator of p. Determine the Cramér-Rao Lower Bound for Var p[ ]ˆ based on one observation from this distribution. c) Show that p= I {1}(X) is an unbiased estimator of p. Does its variance achieve the Cramer-Rao Lower Bound?

Let V = {P(x) ∈ P10(R) : P'(−4) = 0 and P''(2) = 0}. If V=...

Let V = {P(x) ∈ P10(R) : P'(−4) = 0 and P''(2) = 0}. If V= M3×n(R), ﬁnd n.

Please answer all parts of the problem, if possible. Let X ~ Binomial (1, p) 0 <p<1...

Please answer all parts of the problem, if possible. Let X ~ Binomial (1, p) 0 <p<1 a. Show explicitly that this family is “very regular,” that is, that R0,R1,R2,R3,R4 hold. R 0 - different parameter values have different functions. R 1 - parameter space does not contain its own endpoints. R 2. - the set of points x where f (x, p) is not zero and should not depend on p. R 3. One derivative can be found with respect...

Question