If X, Y are two random variables which are NOT independent, then which of the following relations is always true? a. E(X +Y) > E(X)+E(Y) b. E(X +Y) = E(X)+E(Y) c. E(X +Y) < E(X)+E(Y) d. None of these

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A: Factorization Criteriom ( Due to Fisher)Let x⏟= (x1, x2,.....,xn) be a R.S from PME f(xiθ).…

Q: If a random variable X is defined such that: E[(X – 2)²] = 18 and E[(X+1)²] = 33. Then the values of…

A: Given: E( (X - 2 ) 2 )= 18 E( (X + 1 ) 2 )= 33

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A: Expected value is used for discrete or continuous probability function. It is calculated by the…

Q: If a random variable X is defined such that E[(X-1)*]=10and E[(X-2)²]=6, find ux and o?,

A: Consider           EX-12=10    EX2-2X+1=10EX2-2EX+1=10      EX2-2EX=10-1…

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Q: Let X ∼ U(a, b). Use the definition of the variance of a continuous random variable (Equation 2.38…

A: The mean of X is given by:

Q: (iii) If X and Y are two discrete random variables, then E(X + Y) = E(X) + E(Y) provided E(X) and…

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Q: If a random variable X is defined such that: E[(X – 3)²] = 18 and E[(X – 1)²] = 34. Then the values…

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Q: Suppose X1, X2, X3 are m generating functions, Mx, (t) = e²²², Mx, (t) = e²t + 3t², and Mx, (t) = (²…

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Q: 2. (a) If Z = aX + bY and r is the correlation coefficient between X and Y, show that of a*ož + b'ož…

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Q: If X and Y are any random variables with COV(X, Y) = 0.25, o = 0.36, and o = 0.49, then the…

A: From the given information, Covx,y=0.25         σ2x=0.36         σ2y=0.49 Thus,

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Q: X and Y are independent random variables. Determine E[Z], where Z=X+Y. o 1 2 3 4 Px(x) 1/8 3/16 3/8…

A: E(X)=∑ixP(X)E(X)=0×1/8+1×3/16+2×3/8+3×3/16+4×1/8E(X)=0+316+68+916+48E(X)=2…

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A: 4. The given value are EX=0,EY=-1,VarX=1,andVarY=4.

Q: 8. Let X and Y be random variables and let A e B. Prove that the function X (@), if w e A, Y (@),…

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Q: Let X be a random variable with P(X = k) = 1/3 for k = −1, 0, 1. Let Y = X2 . (a) What is the p.m.f.…

A: Given X is a random variable with pmf P(X=k)  =  1/3 for k=-1,0,1 If Y= X2  Find  PMF of Y Are X…

Q: If a random variable X is defined such that: E[(X – 2)²] = 18 and E[(X+1)²] = 33. Then the values of…

A: The given equations are EX-22=18 and EX+12=33. Now,…

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A: Solution: Given, E(X)=E(Y)=E(Z)=1 E(X^2)=E(Y^2)=E(Z^2)=10

Q: If X is a continuous random variable with p. d.f. (X f(x) = }6 ,0 <x< 3 12 ,othewise

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Q: (a) Let X be a random variable and c is an arbitrary constant. Determine the value of c which makes…

A: Dear students as per guidelines we answer the first question only when multiple different question…

Q: If a random variable X is defined such that: E[(X - 2)²] = 18 and E[(X+ 1)'] = 33. Then the values…

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Q: The joint p.d.f of a two-dimensional random variables (x, y) is given by f(x,y) = kxe , 0 0 = 0 ,…

A: To find k, we need to apply total probability =1.

Q: Let X1 and X2be independent exponential random variables: fX1(x1) = e−x1 and fX2(x2) = e−x2 1

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Q: Example 10 : If X is a continuous random variable and Y = aX + b, prove that = a E(X) + b and V(Y) =…

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Q: Example 3: If x1, X2 , ... , Xn is a random sample from a normal population .2 N(µ,1), show that t=-…

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

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