H.W: Define analytically the periodic funtions T/2 1. f(x) 27 37 4 2. f(x) 5 8 4 f(x) 4 6 8 10 12 14 3.

Q: 7. There is a removable discontinuity at x = 1 and f(1) = 4 %3D

A: 7.  There is a removable discontinuity at x=1 and f(1)=4

Q: The equations of the vertical asymptotes of the function with rule f (0) = are: 1+ cos 0 e = 3rk…

A: Take denominator of f is equal to zero.

Q: The domain of the funsfon f(x) te 9) E2,21, or equivalenfly,t243 C) [4,00, 0r )(00,4),or…

A: This question can be solved by applying the concept of existence of function at various points on…

Q: 3t If the Wronskian W of f and g is t²e³t, and if f(t) = t, find g(t). NOTE: Use c as an arbitrary…

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Q: السؤال 1 the function is called periodic function if F(x+t) =f(x), 0 صواب ihi O

A: Please find the answer in the below step

Q: 2. If :|S1, determine the maximum modulus f(:) (a) f(=) =z-2z+3, (b) f(=) == +z-1, (c) f(=)3= :+1…

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Q: Quest The moment generating function of X is given by Mx() = exp(2e - 2} and that of Y by Myt) = (e…

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Q: 18.7. Let f(z) = (e + e-2)/2. Evaluate f(2) -dz, where y is any %3D simple closed curve enclosing 0.

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Q: 15.4.59 Assume that F(x.y,z(x,y))3D 0 implicitly defines z as a for xyz + 8x + - 4z = 0. dz

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Q: Let H(x)=0∫x√4−t^2 dt, for −2≤x≤2. a) Evaluate H(0) b) Evaluate H'(2) c) Use geometry to evaluate…

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Q: Provide what is asked for in each item. 3x (9 – x2) (9 – 3x?)2 54.x(x² + 9) (9 – 3x2)³ * 1. Given…

A: Given:  fx=x39-3x2f'x=3x29-x29-3x22f''x=54xx2+99-3x23 To Find:  a To find the domain of f and the…

Q: 2. Which of the following functions satisfy the hypothesis of Rolle's Theorem on the interval [0,…

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Q: H.W: Define analytically the periodic funtions y 1/2 1. f(x) 27 37 4 2. f(x) 4 f(x) 2 4 6 8 10 12 14…

A: A periodic function is a function that repeats its values on regular intervals or “periods

Q: Let f(x) = e x if −π < x 6 π. And extend f to a 2π periodic function on R. Determine the…

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Q: Suppose that the functions / and g, with linear approximations L, and L2 at x a as shown below. Then…

A: We need to evaluate limx→af(x)g(x)=limx→af(x)limx→a g(x)

Q: If f'(x) = x(x – 5)(x + 1)*, then f(x) has a local minimum at: Select one: а. X = 0 only O b. x = 5…

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Q: 1. Specify the order of the zero z = 0 of the following functions: a) f(2) = z²(e* – 1), b) f(2) =…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 32 Q3: If f(z) Find the residues at all the poles of f(z) !! (Z+2)2(Z2-1)

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Q: The following table shows values of a periodic function f(x). The maximum value attained by the…

A: Note that the function is defined only for multiples of 6.

Q: For the given periodic function give the analytical description of f(t) for the range 0<t<2: -2 -1…

A: Analytical description of f(t)

Q: 2. Consider the following table of a periodic function h(t). t 0 1 2 3 4 5 h 4.0 5.25 6.165 6.5…

A: hmin =1.5hmax=6.5A)Midline:y= hmax+hmin2y=6.5+1.52y=4B)Amplitude:A=hmax-hmin2A=6.5-1.52A=2.5

Q: 9- The general solution for the PDE (DD, + D,D-12D =0 is a. u(x, y) = G,(x)+G,(x+y)+G,(x-y) b. u(x,…

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Q: 2. Show that g(x)= *** has a unique fixed point in [0,1] and find an approximation to the point that…

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Q: 8 Ay 10- Compute the following estimate of f(x) dx using 8- y = f(x) the graph in the figure. 6-…

A: Consider the graph of the function

Q: 3 6. Suppose that f is continuous and that f(z) dz=0 and f(z) dz= 3. Find - 6f(x) dx. -3 -3 -18 18…

A: Given that         f is continuous.

Q: 2. Use the given graph of f(x) = x² to find a number 8 such that if 0 < ]x – 1| < 8. then. [x² – 1|…

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Q: Compute analytically convolution of x(t) and h(t) defined as follows: S 1, if 0 <t< 2, { 0,…

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Q: Which of the following is a saddle point of th f (x, y) = x³ + y³ + 3y² − 3x − 9y + 2 ○ (1,3)…

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Q: 5. Use Green's Theorem to evaluate f. $ (y² – 4x) dæ – (2+ x²y²) dy where C - - is shown below. y…

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Q: 6.Suppose that the joint p.m. f. of X and Y is X- 00 Yə -1- 09 10 Determine: (1)-The value of a;…

A: Given:     x y   0 1 2 -1 0.05 0.1 0.1 0 0.1 0.2 0.1 1 a 0.2 0.05

Q: 40. Eliminate the parameter t from the following and then sketch the graph: x= sin t-6 y = cos t-3…

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Q: 3) See the attached file -1 Vx-1 ,xs 2 ,x > 2 3-Let F(x)= is the function continuos at x=2 A)…

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Q: 4 lim t 4/11+ a. %3D 44 t2 - 16t - b. lim %3D t 4/11- 44 t2 - 16t DNE lim t 4/11 С. %3D 44 t2 - 16t

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Q: 3. Compute x In x da both analytically and numerically. Use trapezoidal, Simpson's 1/3, Simpson's…

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Q: If the moment-generating function of X is a. M(t)=(1–21)"", 1 < ½, Find the p.d.f of X hence use it…

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Q: = 5xte 4 and classify them as Find the equilibria of the difference equation t+1 stable or unstable.…

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Q: Let f(x) = e* if -n <x< T. And extend f to a 27t periodic function on R. Determine the coefficients…

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Q: and that there is a deleted neighborhood U of 0 su and n 2 0. Define f(x) = x -4g(x)(1 – cos x) for…

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Q: 19 Suppose that Ts (x) centered at 2 for f(x) is gien by. Is (X=3+5Cx-2)+8(x-2)²+2G-2)°+(x-2) (3)…

A: T5(x) centered at 2 for f(x) is given by,T5(x)=3+5(x-2)+8(x-2)2+2(x-2)3+(x-2)5

Q: Using the generating function, prove the following relation Ph+1(x) + Ph-1(x) = 2xP(x) + P (x) %3D

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Q: 4.18 Given that g(x) > 0 has the property that 6. show that is a pdf. f(x, y) 2g g(x) dx = 1, (√x² +…

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Q: 1. Suppose that f(z) is analytic for lz <1 and sa Show that there is a constant c < 1 such that…

A: To prove the estimate for }f(z)| over the disc or radius r, center 0

Q: A particular finite difference formula for the first derivative of a funtion is: f '(xi) =…

A: Given: f'(xi)=-fxi+3+9fxi+1-8fxi6h, where xi, xi+1, xi+2 and xi+3 are equally spaced with step size…

Q: Suppose f(z) = (z – i)³e² is analytic inside and on circle |z – i| = 3. Then the upper bound of…

A: Given that f(z)=(z-i)3ez- is analytic inside and on the circle|z-i|=3To find the upper bound of…

Q: For f(x) = √ √2-4 4- ™ Of is not continuous at x = 4 Of is continuous at a Of is continuous at a 5…

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Q: 2t – 2 t2- 1, Let r(t) = - î - tan (t) ĵ+ In(2t) k. %3D (a) Determine the domain of r. (b) Compute…

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Q: Which of the following is a parameterization of the line that passes through the point (1, –3) with…

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Q: $3.1= f R>R; $G) - S Sin Cx) 4x if とこO Show f is di Herntieble oA x=o Find f'co) wing limit…

A: The given function is: fx=sin2x4x, if x≠00       , if x=0

Q: 12. Consider the given periodic function y = f(x), determine a) f(100) b) all value(s) of x such…

A: The given signal is periodic with period T=8. Therefore f(t+nT)=f(t). Here n=12 and…

Q: Which of the following functions has a maximum y value of 4 Oy= 4cos x y= cos 4x Oy= cos x + 4 Oy=…

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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!