6.3 There in a fuzzy bunch of function X 2, 3,4 f (fi, 0.4), (/2,0.5), (fs, 0.9)j Finds (2), 7(3) and 7(4).

Q: Q2] Find the lower bound of Iz - 3|if |z - il < 1

A:

Q: Find the first piece S1 (x) of a natural cubic spline that interpolates the set of points (0,1),…

A: Formula for cubic spline interpolation is…

Q: benefit, issued to (x). Let Zz denote the present value of a whole of life Exercise 4.28 Let Zj…

A: Given that Z1 and Z2 denotes the present value of n-year term insurance benefit and a whole of life…

Q: 4. (a) Show that T and T2 are equivalent statistics if, and only if, we can write T, = H(T1) for…

A: b.  T2 = ∑i=1n log xi      =log (x1) + log (x2) + ... + log (xn)     = log (x1x2....xn)…

Q: 5 UTken the following data in T Table 3 а) 5 UTA TM M f(x) 2 5 UTM 8 2.5 TM 3 1.6989 2.0100 2.5635…

A:

Q: Evaluate / (x - 2y + z) ds. S: z = 3 - x, 0sxs 3, 0sys 2

A:

Q: 2. Let g (x, y) = 2a² – y² . Compute g (1, 2), g (2, 1), g (1, 1), g(–1, 1), and g (2, – 1). - £(1…

A:

Q: A manufacturing company employs two devices to inspect output for quality control purposes. The…

A: A manufacturing company employs two devices to inspect output for quality control purposes.

Q: - Let X1, X2, ...,Xn~N(0,0) and T = Fi (T),Var(T)

A:

Q: 2. Suppose that X is normally distributed with u =-7 and o2 P(X 2x) = 0.84. 14. Find the value of x…

A:

Q: 2. Show that when f'(x) is evaluated at x = Xị, the equation to calculate the unequally spaced data…

A: The step size for the central difference formula is the difference between two consecutive x values.…

Q: 4. Find the cubic spline g(x) for the given data with the ko = 0 and k3 = -12 as given. Xj fi 1 1 9.…

A: Use the following formulae, to find the coefficients of individual splines and the cubic spline…

Q: 1E(X; – Xn)². Prove 1. Let X1,..., Xm,... - iid N(u, T) and consider the MLE în that î, is a…

A: Given X1, X2, … Xn iid N(µ, τ) Given MLE

Q: Q1) Use a suitable Linearization to find the best fit of the form f(x) = Cx3 + for the %3D data:…

A: Given the data,                 (1, -1), (2, 7), (3, 26.3)

Q: 우(4,3) - +xy Elewhere a fivd 우 (s) 6) find p( ys%2 /x= 0:3)

A: A joint probability distribution gives the probability for two variables together which is…

Q: 7.3 Compute P (x > ) from the cdf of X. 7.4 Compute P (x > |from the pdf of X.

A: here calculate constant C using total probability rule  then calculate CDF

Q: 6. Use a substitution to find S (x* + 1)" z³dx.

A: Here we use substitution we find∫x4+111x3dxHere we substitute x4+1=du…

Q: * Consider a piecewise linear interpolation of exp(x), O<=x<=2, with h=0.01; that is, split [0,2]…

A:

Q: 5. (a) Find if y = (In z)". (b) The function f(z) = (In z)=" is an invertible function (you do not…

A:

Q: 1 1 Prove that: L' a exp(a't) erfe( avt), where erfc is complementary a+v error function.

A: Formula Used:- L1t=πsLeat=1s-aLerf(at)=as(s+a)Leatf(t)=F(s-a)                   where…

Q: use the beta function to compute P(3<Y≤5).

A:

Q: A2. a. A company decided to distribute 5 identical computers among its employees. In how many…

A: A2.a.  There are 5 identical computers and three people  We  need to distribute in such a way such…

Q: 0 40 0 0 0 0 40 0 Let S =0 0 0 4 0 Compute s for k = 2, ., 6. 0 0 0 0 4 0 0 0 0 0

A: We can solve this using formula of power of matrix

Q: A manufacturing company employs two devices to inspect output for quality control purposes. The…

A: Given: For X n = 4 p = 0.993 X ~ Bin (4, 0.993) For Y n = 4 p = 0.997 Y ~ Bin (4, 0.997) X and Y are…

Q: Suppose X1, X2, and X3 are independent and N(0.1)-distributed. Com- pute the moment generating…

A: Given function Y= X1X2+X1X3+X2X3 We have to calculate moment generating function

Q: 1- Let X1, X2, X3 have the joint pdf given by 1 eita) ,-c∞ < x1,X2,X3 < ∞ -00 f(x1,X2 ,X3 ) = {…

A: Normal Distribution: A continuous random variable Z is said to follow Standard Normal distribution…

Q: A manufacturing company employs two devices to inspect output for quality control purposes. The…

A: Given: For X Number of trials (n1) = 4 Probability of success (p1) = 0.993 For Y Number of trials…

Q: Q1 Let X1,.,X, f(r;0) = ()0 (1 – 0)2-, x = 0,1,2. (i) Find the score and information functions of 0.…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Let f(x,y,z) = x² e Vy*+ Compute f(3, - 5,3) and f(5,8, - 6).

A: Given that     f(x,y,z) = x2 e√(y^2+z^2)

Q: 1.4 For which values of a eR is the function ar? f(x + iy) = (a'x – axy) +i (- + ay an entire…

A:

Q: 7. (Chapter 12.2, #6) The function f : Z × Z → Z defined by, f(m, n) = 3n 4m. -

A: Given a function f:Z×Z → Z  defined by fm,n=3n-4m. To find the range of the function. We can use the…

Q: (ii) Suppose z = f(x, y), where x = g(s, t), y = h(s, t), g(1,2) = 3, gs (1, 2) = −1, gt(1, 2) = 4,…

A:

Q: 4.8. Show that Dirichlet's function 1, if x is a rational number, { otherwise f(x) = 0, is not of a…

A:

Q: 12. Show that F (x, y, z) = xy +xz + yz has the value 1 if and only if at least two of the variables…

A: This Question is From Boolean algebra where + sign denotes or Operation. So F(x,y,z)=xy + xz+yz if…

Q: M. F O器=醫 ○器=器 P Type here to search

A: To find the incorrect option

Q: 1. If Jis any subinterval of [a, b] and if ø,(x) := 1 for x E J and 4,(x) := 0 elsewhere on [a, b],…

A:

Q: A manufacturing company employs two devices to inspect output for quality control purposes. The…

A: Let the probability that the items classified as defectives and non-defectives by the devices 1 and…

Q: 18. (2) = t"(-t)" dt, show that F(m). m! +1, n+1 %3D m and n are positive integers.

A:

Q: 5.6.10. Consider the function f : N → N, ƒ(n)= n+ (-1)n+1. (a) Compute f(1), ƒ(2), f(3) and f(4).…

A:

Q: 15: Let 8(x) = ,10/t dt 2/x %3D Find g'(In 6). 15552 (A) (In 6)2 15552 (B) (In 6)2 - e$/2 15552 (C)…

A:

Q: the book is "First Course on Fuzzy Theory and Applications"

A:

Q: 7. Suppose that the random variable X have the pdf f(x) = e-/2, x > 0 and 0 otherwise. (a) Find E(X)…

A: Given,

Q: -2 4. Let u = 1 and v = and w = Compute (u x v) x w.

A: Given:  u=-2,1,1, v=1,0,3 and w=-1,1,1   To compute u×v×w

Q: Suppose A=LU. Find t, where: 1 0. 01 [2 3 4 L = 1 0. U = [0 3 1 5 3 01 0 0 1 3 0 4 and A = 1 8. 10 t…

A: given that A=LU…

Q: 2. (a) Check the spline conditions for S1 (x) = 1+ 2x + 3x² + 4x3 S2 (x) = 10 + 20(x – 1) + 15(x –…

A: Given function is  f(x)=s1(x)=1+2x+3x2+4x3    on [0,1]and  s2(x) =10+20(x-1)+15(x-1)2+4(x-1)3 on…

Q: 1 If f(x, y,z)= of then x- y- 3z ду

A: Differentiate wrt y.

Q: 5) Let z = f(x2 - y²). Show that y = 0 ду %3D ax

A: Here, ∂ represents the partial derivative, which means when differentiating with respect to x,…

Q: 3 Let X be a Poisson with parameter 1. Prove (step by step) that P(X < 4) = edr. 1 p³e¬²dx.

A: Given information: PX&lt;4=∫1∞16x3e-xdx

Q: Rouché's theorem for p(z)=z^6−5z^4+z^3-2z ;|z|=1

A:

Q: Q1 Let X1, .. ,X, 2 f(r;8) = (:)0"(1 – 0)²-, x = 0, 1,2. %3D (i) Find the score and information…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.