Let X1, X2, be a nequence of ... independent and identically distubuted rvs, each having frñite mean E[Xc] =M and VCxi) Using chebysher's s inequality , show that P 十メn ... asn->0

Q: 1. (10 pts) For each numerical value below, is the value within the interval (-co,0) ? Answer Yes or…

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Q: Following are temperature (x) in centigrade recorded in a certain city - 10, 8, -6, - 8, 6, 10 i)…

A: Given data is -10,8,-6,-8,6,10Let "x" represents the given data setsample size(n)=6

Q: Apply the Mean Value Theorem [MVT] to the function (x)= vx interval [4, 16]. MVT assures us that…

A: here we have to find the value of Z after applying mean value theorem ,  the given function is…

Q: 2+ex dx ex Evaluate:

A: Topic = Integration

Q: - - Find the largest number ♂ such that if |x − 1] < ɗ, then |2x − 2] < ɛ, where ɛ = 1. δς Repeat…

A: We will find the value of delta.

Q: 2 4 Evaluate Sx dz dy dx 3

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Q: If we approximate e-**dx using Simpson's rule, we get the answer approximately equal Select one: a.…

A: Given: To explain the correct option of the given statement as follows,

Q: 10) tind tre area of tve region boonded by the Graphs Of tre Given functions y- 2-x* ,4= 2-4X The…

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Q: x+k², ifx < 2 What value(s) of k will make f(x) = - continuous? %3D |kx + 10, if x 2 2

A: If the function is continuous then left limit is equal to right limit

Q: Calculate Ls for on the interval

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Q: 95- If f Cx)= X え anel gCx)= |-Va Find fog aned gof a - b- the range and odomain of fog

A: (a). We have f(x)=x2 and g(x)=1-x. Using this, we now have f∘g=1-x2=1+x2-2·x=x+1-2x. Similarly, we…

Q: You are glven the following values of moments : 42 = 43.353, 43 =- 9.774, H4 = 5508.567. Find the…

A: Let  μ2,  μ3  and μ4 be the second, third and fourth central moment. And c is the class interval…

Q: a each of the Find P Gw aned finel the Domain and Range of PEJ. P)=x5 メ2つ Plx) = メ+3 メー2 Vx'-3 P«)=…

A: To find inverse of a function replace all x with y and y with x.and then solve for y

Q: Let Xi take on an exponential distribution: f(x) = theta * exp(-theta*x). Show that the MLE for…

A: Solution

Q: A monotone sequence is convergent.

A: 1) If f is continuous on A then fn is also continuous  on A So The statement is true

Q: If the side of a square X is random with the pdf fX(x)=x/8, 0 < x < 4, and Y is the area of the…

A: The given data: fXx=x8                   0&lt;x&lt;4 Let, Y=gX=X2  Since X is a continuous random…

Q: 12 Given: F : =â, determine F•â. 2

A: r→=xa^x+ya^y+za^zr=x2+y2+z2a^r=r→r

Q: Prop (1.23 ≤ x ≤ 1.72) = Prop (-2.50 ≤ x ≤ 0.5) = Prop (x ≥ 3.00)

A: here use normal distribution table

Q: 2.59 Find || f |sup if a) f(x) = x on (-1, ). So if x E Q, b) f(x) = – x² .2 if x ¢ Q. -

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Q: Inn NTT <os 2. n=1

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Q: 3 In ADU DDL =9mm. Z/=6mmand //=N". Find FD. 3

A: By using the cosine rule we can can find the third side of triangle if we have given the two sides…

Q: I am asked to verify the conditions of the Mean Value Theorem for the equation shown on the interval…

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Q: Hw) if J-0- Gso and X=O+ Cas e Show that Sece+tan 0

A: The given differentiation can be solved by using chain rule. Initially, the y expression can be…

Q: Suppose that fand gare continuous functions such that f(z)dz = 2and s(z)dz = 3, find (2f(2) +…

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Q: Find the average valves of the funce on the qiven intervals: 3. 3 4x+1 gla) =x? E.7 X と

A: We have to find average value function

Q: 2n2 Using the mean-value theorems, show that in sin z w/6

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Q: 33.) Show all steps to evaluate by hand: 4-х2 Vx2 + y2 dy dx

A: We have to evaluate the double integral using polar coordinates

Q: 1. Consider the following intervals on R: A = (0,1); B = (1,2); and C = [2,3). For each pair of…

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Q: Let X- N(10, 5'). What is P(X > 3)?

A: Provided data are,

Q: As PQR in sicle Circl 2²4²25 Such that & & Rone (3,4) &(-4,3) fmd <Q PR?

A: Given that PQR is a triangle, which is inside the circle  such that P and Q are (-4,3) and (3,4)…

Q: (b) Pr[X > 0.6n] < 0.85. Let X be the number of HEADS after n fair coin tosses. Show that

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Q: For any natural number m, evaluate 1/m +x")( 3m 2m 2m +x 2x +3x" +6)"* dx, x > 0. m X

A: Topic:- Integration

Q: 3) A cyclist starts from rest and travels 4 miles along a straight road in 20 minutes. Use the Mean…

A: According to the mean value theorem, in any interval a,b there exists a c such that…

Q: Two RVs X and Y have the joint characteristic function ø.y (@1, 02) exp (-2 w† – 8 ož). Show that X…

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