Suppose that random variables X₁ and X₂ have exponential distribution with expected value of and respectively. Assume that X₁ and X₂ are independent of each other.

Q: Suppose X1,..., Xn are iid with PDF ••• ) f (x | 0) = 404x x > 0, where 0 > 0. Find the MLE of 0.

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Q: ).) Evaluate fxy (-1,2) Given that f (xy)=X Iny. %3D 2) Evaluate fy (23,0,3) for the puncfion…

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Q: A5. The value of the definite integral dx is b) - 8 c) 24 d) 1.5

A: We have to find the value of the given definite integral.

Q: Ex1 Let X .-- Xn be a Sample of x has a density O show that h(x,. )► e (x-x.) is a pivotal Function.…

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Q: d) Find the asymptotic distribution for the parameter h(B) = e® assuming that a is known. 0, e2B B…

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Q: 13- What is the average value of the function f) = sin' X COSX on the interval 0.? 3 a) 27 b) 2 d)…

A: Given function:                     f(x) = sin2 x cos x                              on the interval…

Q: B xe R. Find : 9+x²' Let X - the random variable with the density p(x) = A– - a) A and B; b)P{- 3< X…

A: (a) px=A-B9+x2 it is density function. so px≥0 and ∫-∞∞pxdx=1 ∫-∞∞A-B9+x2dx=1it is even…

Q: (2 cos z-sin z)² dx Evaluate sin z

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Q: Determine h and N to approximate the integral e-t" dt within an accuracy of G 10-5 using the %3D (i)…

A: ∫01e-t2 dt a) Composite Trapezoidal Rule Error=h2b-a12|''Cn ⇒EnTt≤10-5 calculating the derivative;…

Q: 4)Given determine

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Q: PR PR PS PS 10 9. 81 7 6. S' R 1 R' 0 1 2 3 45 6 7 8 9 10 || 5 3. 2.

A: To find the ratio of side length from the given similar triangles

Q: 9. Find the average value of fave of f(x) = x5 on [-1, 1], and find a point in c in (-1, 1) such…

A: 9)  Given  that      Then, the  average  value  of  of   on  [-1,1]  is  given by…

Q: The probalitiy density unction of continous nandon vaniable x given below, Find c according ly- flx)…

A: Solution: From the given information, the probability density function of X is

Q: Find P (12Y<3|X=1).

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Q: Assume that Y,Y1,Y2,...,Yn,..., are iid Uniform from [−θ,θ]. Based on observed data {Y1,Y2}= {−2,1},…

A: * SOLUTION :-  From the above given information we answered as follows

Q: H.W 1)ſ csc*x dx 2)ſ cot*x dx

A: #1) Given integral is∫csc4dx=I (say)

Q: 5) (almost 5.26) Let Y,., Y, be iid with pdf f(yl0) = 0y-2 where 0<0 <y< 0o. a) Find a low…

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Q: S = ÷ S gle) de, then 9 x /1 - xª dx 4

A: The question is taken from the calculus in which we have to solve the integral of given question We…

Q: Let X be a r.v. whose pdf is given by f(x)=C x2 , 0<x<1. Then the normalizing constant C is equal…

A: we have given that  X be a random variable . and pdf of x  f(x)= C x2  ,0&lt;x&lt;1

Q: et X~U([-, 1) and let y = tan(r), show that y Cauchy(0, 1)

A: # using Jacobian transformation we have proved that y=tanx follow Cauchy distribution (0, 1)

Q: 1. 2. µ'n d" $(@) do" in w = 0

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Q: F -10-9-8 --5 4 -3 2-1 G Find the desired slopes and lengths, then fill in the words that…

A: According to our guidelines we can answer only one question or three subparts of a question.other…

Q: Evaluate the tolowing integras using substitution: using OnAiderivat ves 1.

A: Note:   As per our company policy we should answer only one question each time, so please repost the…

Q: let X ~ N(M, 6²) Find MLE (6²) X 7°

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Q: (Hw) ex Test for Exactues ? (ext? + ax) dt+ (2tx* +zt)dx -.

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Q: The following table gives the density of sodium at three temperatures Temp (°C) 94 205 371 Denoty…

A: Given information:The following table gives the density of sodium at three different temperatures.…

Q: 4 The value and their cornesponding of Values of Shown int the table below. are 2 9) Find the least…

A: We have given that,  The data set are : X :- 0, 1, 2, 3, 4 Y:- 2, 3, 5, 4, 6 Then,  We will find the…

Q: Evaluate the integral S de using the two-point Gaussian quadrature rule

A: For the integral I=∫abf(x)dx, the Gaussian quadrature 2-point formula is,I=b-a2w1fm1+w2fx2where…

Q: I Find marginal di stributon for x Find Condi tion al pdf fyx ) E E slimade plosy< /x0) I Eslimale…

A: As per our company guidelines, we are supposed to answer only the first 3 sub-parts. Kindly repost…

Q: () Gue an example Where Int CAUB) E intCA)u int(8)

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Q: Ex2: a) Consider the Rayleigh distribution: f(y) = 21/²2 82 Show that the CDF is given by: -20 12…

A: Objective of this question is that, we should construct 100(1-ɑ)% CI  for population parameter θ

Q: 2. Which definite integral approximation formula is f(x) dx = Left rectangles Right rectangles…

A: The given formula is;  Integration of f(x) , limit from a to b = (b-a) /n [y0+y1+y2+y3+...+yn-1].

Q: Q3/ Evaluate 2 vsinx dx, using i- Trapezoidal rule ii- Simpson's 3/8 rule Ans. 1.1615

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Q: Q2. In the bank example in page 44-45 of the slides, the joint pdf of X, Y i given by 6 fxx(x, y)…

A: a) The marginal pdf is calculated as follows: fy=∫xfx,ydx=∫0165x+y2dx=65x22+y2x01=6512+y2…

Q: 1. E(1,000 Zz) =? .04, a) d₁ = .05, b) μlx+t= .06. .07. t 10

A: Given     δt=0.04,   t&lt;100.05,   t≥10 μx+t=0.06,   t&lt;100.07,   t≥10