Suppose we taken a random sample of size n from Bi(m,p). Find the CDF and PMF of X(r)

Q: A random sample of X1,X,, X,...,X, have mean E(X,)= µ and Var(X,)=o². Given the value of §² ¿(x, -…

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Q: Let x and y be two independent N(0, 1) random variables and Z = 1+ X + XY², W = 1+ X. Find Coy(7,W).

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Q: Suppose X and Y are random variables with E[XY ] = 6, E[Y ] = 4 and E[X] = 5 Find Cov(X; Y )

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Q: Consider the model y = Bi +x2B2 + x3ß3 +e and suppose that application of least squares to 20…

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Q: Solve the given SLE using LU-Factorization X, +x, +x3 = 3 X, - x, + 4x; = 4 2x, +3x, – 5x; = 0 -

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Q: We draw 8 cards, one at a time, randomly, and without replacement from an ordinary deck of 52 cards.…

A: The number of cards in a deck is 52. Xi = { 1 if the ith card drawn is a heart, 0 otherwise

Q: If X is a random variable, prove that Cov(X,X) = σX².

A: Let X is a random variable.

Q: Suppose that X,, X2, .., Xm and Y,, Y2,..., Y, are independent random samples, with the variables X,…

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Q: Let X1, X2, ..., Xn be an independent random sample from n(µx,ox), and Y1, Y2, . .., Ym be an…

A: Given X1,X2,...,Xn~N(μx,σx2)Y1,Y2,....,Yn~N(μy,σy2) are two independent random samples.   Denote…

Q: 1. Consider the thresholded AR(1) process J01a1-1 + wi if ai-1 < 0 01xt-1 02x1-1+ wi if x-1 20 where…

A: Given the threshold AR(1) process xt=θ1xt-1+wt     if  xt-1&lt;0θ2xt-1+wt     if  xt-1≥0 where wt is…

Q: 5. The Gram-Schmidt process applied to {ri, va} = {(G) · 6)} results in {u1, u2} = V2 {m, u2) = {()…

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Q: Given: X and Y are random variables with PI,Y -.75, o = 96, and Oy = 114. %3D a) Draw a rough…

A: Cov(x,y) =ρx,yσx×σy=-0.7596×114=-8208

Q: (8.20 ds: Find the tayLor seri's expen sian of In Cxri) about XozO

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Q: X... X, are random variables, then prove that yar| X = var (X) + 2 cov (X, X). j+k k-1

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Q: Let the random variables (discrete) X1, X2 have the joint pmf p(x1, x2) = 1/3, for (x1, 12) =…

A: Covariance is given by, Cov(X1,X2)= E(X1)*E(X2)-E(X1*X2) E(X1)= (summation X1*p(X1,X2)) =…

Q: Let X and Y be random variables, and a and b be constants. a) Prove that Cov(aX, bY) = ab Cov(X,Y).…

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Q: If X is a random variable with characteristic function ox (w) and if the 'r'th moment exists, it can…

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Q: Suppose that each year, 80% of residents living in state A stay in state A, while 20% of them move…

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Q: Consider a random sample X1, X2, ..., X, from Bernoulli's distribu- tion B(1, p). Prove that X; is a…

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Q: Consider the matrix N formed when solving for coefficients of the Newton interpolating polynomial.…

A: Consider the given data points, 0,3, 1,-2, 2,5 and 3,4 Make the table of Newton interpolating…

Q: Suppose you have joint random variables X and Y. a) If a problem does not state anything about…

A: X and Y are 2 R.V. and if the dist. of X is not influenced by Y values then 2 R.V. are independent.

Q: Let X and Y be jointly Gaussian random variables with PDF exp { (12 + 4y² – 2x + 1) } fx,y(x, y) for…

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Q: 2. Suppose that y, and y, have a nonzero Wronskian and that cik2 Y, = C1Y, + c2Y, and y, = kiy, +…

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Q: Let X1, ..., Xn be IID from Uniform(θ1, θ2). Use the method of moments to estimate θ1 and θ2, the…

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Q: Solve the given SLE using LU-Factorization X + x2 + x3 = 3 X, - x2 + 4x, = 4 2x +3x, — 5х, %3D 0 |

A: Given SLEx+y+z=3x-y+4z=42x+3y-5z=0convertit in to matrix form1111-1423-5xyz=340convert it in to…

Q: 1. Compute the first two steps of the Jacobi and the Gauss-Seidel Methods with starting vec [0,...,…

A: system to solve using Jacobi and Gauss-Seidel Methods : 2u-v=0  -u+2v-w=2  -v+2w=0

Q: Consider the following LP model. Min Z = 3x1 - 2x2 + x3+2x4 s.t. x2 + 4x4 = 40 2x1 - x2 + 4x3 + 2x4…

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Q: Let X - Bernoulli(p) and Y Bernoulli(q) be independent, where 0 < p, q < 1. Find the joint PMF and…

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Q: Let X, and X, be two exponential rvs with common parameter 1= 1. 2 1) compute P(X, < 3) and P(X, <…

A: As requested i have answered 1st part using concept of exponential distribution.

Q: 2. Solve the given SLE using LU-Factorization X, +x, +x3 = 3 X, - x, + 4x, = 4 2x, +3x, - 5x, = 0…

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Q: Let X1 and X2 be independent random variables for which P(Xi = 1) = 2/5 and P(Xi = 2) = 3/5 . Define…

A: Correlation Coefficient between two Random Variables: If X and Y be two random variables, then the…

Q: Let X1,., Xn be independent and identically distributed random variables with Var(X1) < o. Show that…

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Q: 4. A random variable T is selected.Tis uniform on [0, 1]. A second variable U is chosen that…

A: Given  A random variable T is selected.Tis uniform on [0, 1]. A second variable U is chosen that…

Q: Solve the given SLE using LU-Factorization X, + x2 + x3 = 3 X, - x, + 4x, = 4 2x, +3x, – 5x; = %D

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Q: Let X1,..., Xn an iid random sample from Gamma(a, X). Show that [I-1 X; and E X; are jointly…

A: Given:  random variables Xi (i=1,2,....n) are iid from gamma(α,λ) then to show that ∏Xi and ∑Xi  is…

Q: 2. Let X1, X2, X3 ., X, be iid b(1, p) random variables. Let S, = E=1 X¢ then prove that Sn-E(Sn)…

A: From the given information, X1, X2,.....,Xn be iid b1,p random variables. The probability mass…

Q: Determine all the values of m and n for which the complete bipartite K(m,n) is Hamiltonian, and for…

A: We know that,  Km,n is Hamiltonian if and only if m=n and n is greater than or equal to 2.

Q: 4. A random variable T is selected.Tis uniform on [0, 1]. A second variable U is chosen that…

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Q: Suppose X1, X2, ..., Xn is an iid sample from fx(x\0) = 1 -e-lel/ª I(x € R). 20

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Q: Suppose X is a discrete random variable with pmf defined as p(x) = log10 fo x = {1,2,3,...9} Prove…

A: A pmf is legitimate if (i) 0≤P(x) ≤1                                   (ii) ∑P(x) =1

Q: Consider a LU factorization of 3 A = as A=LU. Then L2,1 and U1,1

A: We have to find values given in the question from the matrix.

Q: 4. Let X, Y be independent random variables. Prove that E(XY) = E(X) E(Y) and hence show that V(X…

A: The expected value is also known as average of the probability distribution function. It is the…

Q: if x,x2, ... .., Xp be a random sample from Bin( 1,0). Show that T =i is UMVUE

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Q: Sketch the ensemble, that is, realizations of the random process X(t) = A cos(2πft), where f is a…

A: Answer:

Q: Let X1,..., Xn an iid random sample from Gamma(a, X). Show that II1 X; and Xi are jointly sufficient…

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Q: random variables with E(X) =2, E(Y)=3 ,V(X)=4,V(Y)=16. Find a)E(5X-Y) b)V(5X-Y) c)COV(3X+Y,Y)…

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Q: Show that the T(x1,x2,..xn) =x² – is UMVUE of u? with variance - 72

A: Given information: The investigator is specially interested to find the UMVU estimator.

Q: 4. Assume that X is an exponential random variable. Suppose further that Var(X) 5- E(X). (a) Find…

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