6. Let f be defined as 0, -1 < x < 0 f(x) = { x +1, 0

Q: 5) Let -{2 1 Find the Fourier series of f(x). f(x) = -TAMO. 0 < r < π.

A:

Q: EX: - Derermine expoentail fourier series of X(t)=exp(2t) for -1<t<1 and has period of 2

A: Find the attachment for the solution.

Q: [xus (2) x+10) xuIsx(p) x(1) (k)1 ×sinx (1x [x][a] (k) 1 x (m)xcosx

A:

Q: 23// Expand f (x) = –x – n , -n<x< 0 in a half range sine series and Find its Fourier series

A:

Q: Given f (x) is defined as a half range Fourier series - x2 ,0 < x < 1 f(x) = x – 1, 1<x < 2 Sketch…

A: Even extension of a function is the same graph repeated in the remaining part of the interval.…

Q: 5. Consider the following function : x 0 (a) Calculate the Fourier series (both sines and cosines)…

A:

Q: Express f(x) as a Fourier series in the inerval 4 %3D 12 - T<x<T

A:

Q: x) = cos in the interval of (-T, 7) %3D

A:

Q: - 2 sxs-1 QI/ Find the Fourier series for the Function f(x) = 1 -1sxs1

A:

Q: Q5): Determine the Fourier series of the function f(x) = 1 - x² in the interval [-1, 1].

A:

Q: Write the double Fourier series if f(x, y) = x²y², -<x<n, -n<y<m

A: We are given the following function.         f(x, y)=x2y2,  -π&lt;x&lt;π, -π&lt;y&lt;π Now, we need…

Q: Develop f x in the Fourier series, if defined as: (i) : f x = sinx, -T <x <T. -k, if -1<x <0, (k, if…

A:

Q: 3) Let f (x) be defined as -1 < x < 0 f(x) = (0, lx + 1, 0<x<1 a) Find the Fourier series of f,…

A: A Fourier series is the series expansion of a periodic function in terms of sine and cosine…

Q: Calculate the first few terms of the Fourier series of f (x + 7) = f(x) Enter simplified expressions…

A:

Q: (b) You are given that the Fourier series for f on the interval (-7, 7) is [a, cos(nx) + b,…

A:

Q: f(x) =1; (0<x < n) = 0 (a < x< 2n)

A: In the given question we have to find the Fourier series of the peicewise function s.t…

Q: 4х Obtain the Fourier series for the function f(x)=1 1+ 3 <x< 0 2 1A. and 4.x ) <x < 3 f (x+3) =…

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Q: 5 5 Interval: 0 <x<3

A:

Q: Determine the Fourier Series of f(x)= { = *R 0<x<T π < x < 2π Interval: 0<x<2*

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Q: Q4/ A: Find Fourier Series of the Function: f(x) = {-K -TAX<O 0 <x<*

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Q: 2х - 2 -1< x<0 f (x) = {-2x – 2 (5 (x+2) 0 <x<1

A:

Q: Let /(x). +z, -=<I<0, 1- -*+2 OSZ<*. (a) Sketch the graph of f. (b) Find the Fourier series of f.…

A: The given problem is to sketch the given periodic function and also to find the Fourier series…

Q: Find the Fourier series of the following f(x) on the interval [-1,1]. f(x) = –4+ 4x2

A: Recall: Fourier series :   f(x)=a0+∑n=1∞an cosnπxL+∑n=1∞bn sinnπxL ; -L≤x≤L where , a0=12L∫-LLf(x)…

Q: Let ● 0 { (x - 1) Compute the Fourier cosine coefficients for f(x). Ao = -16/5 f(x) . . = • An =…

A:

Q: (2-x,0<x<2 f(x) = {²0₁2<x<4 Periode = 4

A: The given function is                     f(x)=2-x, 0&lt;x&lt;20, 2≤x&lt;4    Period = 4

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!