Exercise 1: 1. Let X: Poisson(@), show that whether the p.d.f of X is a member of exponential class or not. 2. Let X: U(0, 0), show that whether the p.d.f of X is a member of exponential class or not.

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Q: Alog f(x) = log[1+ Af(x), f(x)

A: We have to solve given problem:

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Q: b) Is the Soluticn increasing or P N decreasia a when between o and te canyjug capacity

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Q: Consider the function g defined by 1 g(x, y) = cos (Tx)+ log3 (x - y) Do as indicated. 1. Determine

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Q: Let f be the exponential function defined by (2+2) f(2) = () and determine the folloving information…

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Q: 1/x e 7 dx y3 -1

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Q: 2. Evaluate (hint: use beta function) y°V6? – y²dy

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Q: Assuming that Switzerland's population is growing exponentially at a continuous rate of 0.23 percent…

A: Let x(0)=Initial population=6.6 millionlet a=birth rate-death rate=0.23 expression of population…

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A: The given statement is false. Therefore the second option is correct.

Q: 01. A gardener was observing thd behavior of the roses that he transplanted a week ago. He observed…

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Q: Let f R*R, defined by f(x) = 3*, then f(x) = %3D O log,3 3* o log3x log3

A: See solution below.

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Q: Which of the following formulas describes an autoregressive (AR) process?

A: Write the AR process (autoregressive process) of order p

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A: Use continuity definition of function

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A: We need to find the values of x for which the following inequality holds good.

Q: 3. If the pdf is -a<x<a , Find the generating function( express your answer in simplified form)

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Q: Show that -E{t, log(sigma(w*x)) + (1 – t;) log(1 – sigma(w"x;))} = E, log(1+ e-yw* x %3D Where…

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Q: 5. The natural logarithmic function f(x) In x has the %3D asymptote x %3D

A: Given function - f(x) = ln(x)

Q: Evaluate (a) by using beta function ∞ ∫ √xe−xdx 0

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Q: The logistic function given by f(x)=1/(1+e^-x) is a bijection, whose domain is R and range is (0,1).…

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Q: Define Beta function and hence, find x° V1– x²dx.

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Q: 9. (a) Show that if a > 0 and a + 1, the function f(x) = a® is a 1-1 function. (b) For a > 0 and a +…

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Q: 5. Prove if the following function is differentiable y = x loge-*

A: Given that: y=xloge-x

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Q: The natural exponential function f(x) = e", has domain and range as: O Range = R and Domain = (0,3)…

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A: This is a problem of finite math, and complexity.

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A: Solution of given question is written in below steps.

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Q: (a) Show that z = 0 is the unique branch point of f(z) = log(z)

A: Since you have posted a multiple question ,I will solve the first question (i.e(a))  for you. To get…

Q: . Consider the function g defined by 1 g(x, y) = cos (Tx y) + log3 (x - y) Do as indicated. 1.…

A: As per policy, we are allowed to answer only 1 questions at a time. So, I am answering the first…

Q: Find constant A such that log3 x = A log5x , for all x &gt; 0.

A: To find the constant A such that the below equation is true for all x&gt;0.

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.