If f = xi+ yj+ zk,1Fl =r,and n =, then show that grad (E) == %3D

Q: Find C1, C2, and C3 so that the given functions will satisfy the prescribed initial conditions.

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Q: A 2³-2 design was used to investigate the effect of A = condensation temperature, B = amount of…

A: Since, you posted multiple questions, we will solve 3rd question for you.

Q: The ODE ty" – 3ty' + 3y = t* has a particular solution Yp(t)

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Q: Could someone explain how they go to value for Z sub alpha/2 in this Problem 18a?

A: Here we have to find critical value Zα/2

Q: Find the values of x,y and z using Gauss Jordan method.

A: We have given a system of equations ,  3x + 4y + z = 102x - 3y + 5z + 9 = 0x + 2y - z = 6 This…

Q: If x¨ + x˙ − 6x = e ^−t, with x (0) = x˙ (0) = 0, what is X (s)?

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Q: 1. Compute E(1/X) 2. Find the cdf and the pdf of Y = 1/X 3. Compute E(Y) and compare this result…

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Q: In the OLS technique why we minimize E ɛ² instead of a) E e²; b) E ɛ ?

A: In Ordinary least square estimation we generally minimize sum of squares of residual......

Q: If T(x)be an estimator of 0, then bias term can be defined as, 0- E[T(x)] E[T(x)]=® E[T(x)]-®² a) b)…

A: Solution: Unbiased estimator: A statistic T(x) is said to be an unbiased estimator of θ if E [T(x)]…

Q: Prove the following: (a) E (C X) = Č E(X) (b) E (X + Y) = E(X) + E(Y) (c) E (XY) = E(X) · E(Y) When…

A: Answer: For the given data,

Q: In a mixed reactor, the concentration of a chemical is given by: C = Cin(1-e-0.025t) +c(e-0.025t)…

A: Solution for a: Given function is c=cin(1-e-0.025t)+c0(e-0.025t)                         (1) we have…

Q: Let SINGLEDFA = { | M is a DFA and for all s e L(M),|s| = 1}. Show that SINGLEDFA is decidable.

A: Detailed explanation mentioned below.

Q: Find P(2 0

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Q: Estimate the value of E-2 (1/(n² + 4)) to within 0.1 of its exact value.

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Q: A radioactive sample decays according to the law - -hy where k>0 Suppose c represents the size of…

A: From the given differential equation:   dydt=-ky   So, dy=-kydt...Integrating on both…

Q: Given the auto correlation function for a stationary ergodic process with n. periodic components is…

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Q: For the sum п-1 n n+1 ΣΣ(1+ j=1 k=j+1 l=j that we encountered in the analysis of the running time of…

A: During the calculation of running time of Gaussian elimination, we encounter the sum…

Q: 3. The value of c is given by Vn А. /n+1

A: This is a limit problem

Q: 1. Prove e'e increases when a restriction, RB = q, is imposed on the regression coefficients

A: Given: The regression Y=Xβ+ε, where ε is a vector. when a restriction Rβ=q is imposed on the…

Q: Find the value of k that makes the antidifferentiation formula true. |(1- 10x) 1 dx=k In |1– 10x| +…

A: According to question given that ∫1-10x-1 dx=k ln1-10x+C

Q: QUESTION 5 Select all valid answers. d. 5x°+8x4+2 Compute dx 10x'+11x +8 n (45x8+32x3)(10x7+11x…

A: We have to find derivative

Q: If R = 3, C = 3, and alpha is set at .05, what would the critical value be for a chi-square test of…

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Q: f substance B, in milligrams, left after t years, given that the initial quar

A: Option of part c is A.

Q: Solve the following evaation for a 2メ+S X +1 e 3De

A: We have to find the value of X.

Q: FIND THE GENERAL SOLUTION OF THE D.E.

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Q: A- Find the integrating factor of the following D.E 2

A: a) Here we have to find the integrating factor of given differential equation:-  We have,  Compare…

Q: If P(x) = -1/x then the integrating factor is a. e-* 1 b. С. -x d. e-1/x

A: Consider the linear differential equation: dydx+pxy=qx The integrating factor for above linear…

Q: If 8(x) = [e²-m (21+ - dx S[e²-In (21+1) ]dt, find g(x). -2 A e-In(2x+1) 4 B (2x + 1)² 2 Ⓒ (2x + 1)²…

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Q: If g(x)=- A B d- ſ ^ [e' − In(2t + 1) ]dt, find g*'(x) . dx -2 2 (2x + 1)² 4 et + (2x + 1)²…

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Q: Let X ~ T(a, B). If E(X) = aß and E(X²) = aß² + a² ß². If â = X, find the method of B moments…

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Q: 2.16 Find the characteristics of each of the following PDES: a?u a?u (a) +3 + 2- - 0 ay? dx? дх ду

A: ** I believe we are being asked to classify the above given PDEs into elliptic hyperbolic and…

Q: For a given process, it is possible to have a value of Cpk greater than the value of Cp at the same…

A: In general, the value of cp is always grrater than the value of cpk.

Q: Consider the potential outcomes for each individual i: JY₁i Yoi Y₁ = D₁ = 1 Di = 0 1. Write the…

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Q: The populations, P, of six towns at time t in years are given by(i)   P=2,090(1.08)t(ii)…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: If X is an exponential r.v. with parameter 5, identify the r.v. 10X

A: Introduction: The random variable X has an exponential probability distribution with parameter, λ =…

Q: In order to maximize tomato yield we are interested in whether using different cultivars of tomatoes…

A: Formula for MST: MST=SSTdfSST From the given information, SST=165 and there are 3 df. That is,…

Q: If f(x) = x(e*+) , then f'(x) = %3D (A) (e + x³) x(e²+x²-1) (B) (e" + 5x*) In(x) æ(c*+z*) (C) (e* +…

A: To find f'(x) for the given function

Q: Given that X has pmf f(x)=1/(2)^(x+1) , x=0,1,2,... and et<2 , use mgf technique to…

A: Given: X has the pmf as follows, f(x)=1/(2)^(x+1) , x=0,1,2,...et&lt;2

Q: Calculate E(X³), where X has the following PMF: .5 x=1 f(x)=.3 x=2 2 x=3

A: Given that  PMF of X is  x 1 2 3 f( x ) 0.5 0.3 0.2

Q: d If g (x) = ª[e' - In(21 + 1)]dt, find g(x) . dx A e-In(2x+1) 4 (В et + (2x + 1)² 2 (C) (2x + 1)² 4…

A: Topic:- application of integration

Q: Q1: Let X have p.d.f ==,x = 1,2,3 and X, and X2 are stochastically independent. Let Y1 = X,X2 and…

A: Given Information: Let X have pdf; fx=x6; x=1,2,3 X1 and X2 are stochastically independent. Y1= X1X2…

Q: The population of two different species are given by P1 P1 = 4e0.6t - and P2. where t is measured in…

A: The population of two different species are given by, P1=4e0.6tP2=9e0.4t

Q: If we use a linear approximation of e- at a = 0 to approximate e-1/3, then we obtain: А. 4/3. В. 2/3…

A: The solution is given below

Q: Find P(2 0

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Q: If we know that E (") (x" 1) = ("†").t then show that Eo (") -C") r3D0

A: Given information: The given theorem is:

Q: Given a J. p. d. f. of x and y: f(x,y) = {e- (x + y) x and y are stochastically independent. True…

A: Joint pdf is given, We have to tell For the following function, x&amp;y are stochastically…

Q: Find the initial value of f(t), if: 2(s + 2) s(s + 1)(s + 3) F(s) = -

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Q: A) Vn +5 B) is larger than Vn + 5 1.

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Q: e: ZN ZP

A: Given: MN¯≅MP¯, NO¯≅PO¯ To prove: ∠N≅∠P

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!