Let X N, 02). The pdf of X is given by f(x) = √2π0² (a) In class I showed that E[X] = . Show that Var (X) = ²

Q: A- Explain the following • Random Experiments. • The Variance of data. Bayes' Theorem.

A: 1. Random Experiments: A Random Experiment is an experiment, trial, or observation that can be…

Q: f is a differentiable function. Then (х) dx ef(x) + C el(x}+C f'(x)ex) + C f'(x) + e(x) + C f(x)ex)…

A: topic - integration

Q: Show that for some number a > 1, we have 1- <= In(a) <= a – 1. Hint: In(a) = S"dx, please check the…

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Q: if r >1 Suppose f(x) = Determine whether f'(1) exists. x? if r < 1.

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Q: Given that f(x) = x"h(x) h( – 1) = 2 h'(– 1) = 5 Calculate f'(– 1). Hint: Use the product rule and…

A: Given that: f(x)=x11h(x)h(-1)=2h'(-1)=5

Q: Suppose h is a function that is differentiable for all real numbers x, h(2) = 7, and h'(2) =-2. What…

A: Final Answer: The value of dxd​[xh(x)​] at x=2 is 4−11​ Option B is the correct answer. B) 4−11​…

Q: Show that, for any constant k, f(x)' dxL k f'(x) k

A: To show: For any constant k, ddxf(x)k = f'(x)k

Q: 6x2+5 If f(x) = In x4/5 find f' (x).

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Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: Let f (t) = e Use the results of Section 3.2 to find the derivative of f at the given numbers. Give…

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Q: In x

A: A detailed solution is given below

Q: Use the following information about Wal-Mart stock. 52 weeks VOL NET HI 52.05 LO STOCK 41.69 WMT DIV…

A: First, we need to calculate the cost of the shares without the broker's commission. This can be done…

Q: 7 x + 2 Let f(x) = x4 . x + 5 f'(x) = %3D

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Q: Compute f(s), where f(x) = cos oz and 8 >

A: We have to find out the Laplace transformation of f(x) = cos

Q: b. foet t'dt

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Q: 7 Find the most general function F such that F'(): - 5V?.

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Q: Let Ximexp (A). Show i Sulficieny that T-ZXi is Statistics

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Q: Let h(x) = In[(f(x))² +1. Suppose that f(1) = -1 and f' (1) = 1. Find h'(1).

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Q: Given that f(x) = x²h(x) h( – 1) = 4 h'( – 1) = 7 Calculate f'( – 1). Hint: Use the product rule and…

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Q: Find the function f(x), such that f(x)= In(3x) J ƒ(1)=1.

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Q: Let X ~ Gamma (8, 2) . Then E |[X²] is equal to

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Q: The tangent line to the graph of some function f at x = 4 is y = - 2x + 5 corresponding normal line…

A: Given query is to find the equation of the normal line.

Q: Suppose F(8) = 5, F(9)= -23, and - 9 f6f (x) d Your Answer: Answer dx= F'(x) = f(x).

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Q: Let f(x) = t° dt. Evaluate the following. f'(x) = f'(5)

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Q: Let ø be a C' function, and suppose 00 $(x) = >, b,Un(x)., ø"(x) = ), cnUn(x). %3D n=1 =1 Express…

A: Here in the question it is give that ϕ is a C1 function .  Consider the given function as follow:…

Q: Fuppose that f'(x) = Vx +4 for x>0, and that f(1) = 1. Find f(4).

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Q: Let f (x) et . Find a so that f'( a ) = 0. Hint: use the quotient Rule.

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Q: Suppose F(x) is between 4 and 8 for x in [3,12]. What is the largest that · 12 L" F (x) dx can be?

A: given that function F(x) between 4 and 8 for x in [3, 12] we have to find the largest value of…

Q: Let f(x) = 7x° In(x) + 3 5 f'(x) =

A: We have to find

Q: Let f(x) = x°e*. Find f '(x).

A: Product rule:d(uv)dx=udvdx+vdudx

Q: Use this definition to find f'(a) at the given number a. f(x) = V3x + 1, a = 8

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Q: Differentiate the given function: f(x) = In(2r³ – 5æ) 6x² – 5 A f'(x) = 2x3 – 5x 1 ® f'(x) = 2x3 –…

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Q: if r>1 if r< 1. 6) Suppose f(r) = Determine whether f'(1) exists.

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