A random sample of size n = 225 is to be taken from an exponential population with θ = 4. Based on the cen-tral limit theorem, what is the probability that the mean of the sample will exceed 4.5?

Q: 1. Use the Nth-Term Test to examine the divergence of: n n+1 n=1

A: Follow the steps and just remember the form of the nth tems test.

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A:

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A: From the given information, fY(y)=ye-y22, y>0 And X=klog(Y)Xk=logYeXk=Yexk*1k=dydx

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Q: Theorem 64. Let {pk}1 converge to point If y # x, then {pk}1 does not converge to y. x.

A: Given that sequence pkk=1∞ converges to point x.

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A: Here we have to find Riemann sum left Endpoints

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Q: 4. Suppose that O is a uniform random variable on the interval (-1/2,1/2). Let T = tan 0. Find the…

A: Solution

Q: The series: (-1)" tann n=1 Da. converges absolutely Db. converges conditionally Dc. diverges 8.

A: Answer is following.

Q: Question 9 For n21 and r E R, let fn (x) = 1+n?r?° (a) Show that (fn) converges on R. (b) Is the…

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Q: Apply the ratio test to the series. n! 2n3 n=1 an+1 Find the limit lim an

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Q: Calculate the Radius and the Interval of Convergence na" 2n n=0

A: we will be using ratio test for the series to converge.

Q: IF X has an exponential distribution with the parameter 0 an Hy = 202, where 0 >0 then find µx, a,…

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Q: - - For what values of p does dx converge? 1

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Q: 51. For which values of a does eax dx converge?

A:

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A: This question is about application of powers in signals

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A: Given, If the function f(x)=x-2 ,1≤x≤6 with n=5

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A:

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Q: 4. Which comparison would show that dx converges? x + e*

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A: Given, Mxt=λλ-tr As we know that, Ex=Mx'0Ex2=Mx''0 Now, Mx't=ddtλλ-tr=rλrλ-tr+1

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A: The decay model is represented by,

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Q: 1 -dx x In*(ex) 1. e

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Q: Ln=0*

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.