Use the inner product < f,g >= = f(x)g(x)da in the vector space Cº[0, 1] to find the orthogonal projection of f(x) = 2x² + 4 onto the subspace V spanned by g(x) = 1 - proi (f) and h(x) = 1.

Q: Show by an example that (AB)" B™A".

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Q: Suppose Var(X) = 32, Var(Y) = 47, and X and Y are independent. What is Var(.15X + .85Y)?

A: Given, a  and . and  are independent random variables.It is required to find the .To solve this…

Q: uppose Var(X) = 93, Var(Y) = 98, and X and Y are independent. What is Var(.6X + .4Y)?

A: Answer: - Given,  Var(X) = 93, Var(Y) = 98, and X and Y are independent.                 What is…

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A: The order of surd is indicates the index of root to be extracted. For example: n√(x) here n is…

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A: Let u and v be the function of x  Then∫uvdx=u∫vdx-∫(dudx∫vdx)dx

Q: showthat

A: The solution of the asked question is given as

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Q: Suppose Var(X) = 88, Var(Y) = 17, and X and Y are independent. What is Var(.28X + .72Y)?

A:

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Q: Remainder must always be either less than or equal to the divisor. true or false

A: Remainder must be either less than or equal to the divisor . The above statement is true .

Q: Differentiate 2xー4x -

A:

Q: 3 Evaluate: (12t3 – 12t2 + 6)dt

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Q: Find the largest damain af the function : 2X+2X-1 x²+3X-10

A: Given  y = 2x2+2x-1x2+3x-10 To find the domain of the above function, we have to find the value of x…

Q: Suppose Var(X) = 52, Var(Y) = 41, and X and Y are independent. What is Var(.89X + .11Y)?

A: Given: Var(X) = 52 Var(Y) = 41 X and Y are independent. Formula Used: VaraX+bY = a2Var(X) + b2Var(Y)…

Q: Evaluate [ V21+12x-9x²dx

A: The given integral ∫21+12x-9x2dx can be evaluated as, ∫21+12x-9x2dx=∫21+-9x2-43xdx…

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A: f(x) is the probability density function if the area under the curve is one and f(x)&gt;0

Q: Suppose Var(X) = 43, Var(Y) = 36, and X and Y are independent. What is Var(.67X + .33Y)?

A: GivenX and Y are independentVar(X)=43Var(Y)=36

Q: Suppose Var(X) = 4, Var(Y) = 78, and X and Y are independent. What is Var(.58X + .42Y)?

A: Answer: - Given, Var(X) = 4, Var(Y) = 78, and X and Y are independent.                What is…

Q: Compute r2

A: Given the calculated values, t value, t = 2.17

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A: Given a statement

Q: (AUB) = ACNBC. Show that P(ACNBC) = 1- P(A) - P(B) + P(ANB)

A: P(Ac∩Bc)=1−P(A)−P(B)+P(A∩B)

Q: Suppose Var(X) = 71, Var(Y) = 12, and X and Y are independent. What is Var(.59X + .41Y)?

A: The objective of this question is to find the variance of the linear combination of two independent…

Q: Example. Differentiate f(r) = (4r"-5x+4(72-z). n

A: The given function is fx=4x3-5x2+47x2-x.

Q: xp áp (** + 1. y+1 x2+1,

A: Changing order calculate the integral:  ∫14∫12xy+1+xx2+1dydx=∫12∫14xy+1+xx2+1dxdy…

Q: 4sqrt(2) was incorrect

A: Given:= f(x,y) = x3y2U = (-3,3) P= (-1,-2)   The directional derivative being negative means that…