Let X1 and X, be any two random variables, then V( X1 + X2 ) must be: OA. greater than: V(X1 ) + V(X2). 3. equal to V(X1) + V(X2 ).

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

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Q: Suppose for a certain random variable, X, we have V( X) =1. then which of the following is a true…

A: For a certain random variable, X, we have V(X)=1.

Q: Let X be a discrete random variable with the following pmf k = -2 5 k= -1 k = 0 P(X = k) = * k-1 1…

A: Solution: Define  Y=(X+1)2 The plug the values of X=--2,-1,0,1,2, inY=(X+1)2 the new values of Y is…

Q: 2. Let X be a random variable. Is it possible that px,x² = 1 for some X? What about PX,x² = -1?

A: Solution

Q: 2. Let X1, X2, X3 be three independent random variables with means ui -5, µ3 tion of Y = X1 - 2X2…

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Q: 2. Let X be a random variable with E[X] = 15 and Var[X] = 10. Suppose Y = 2X – 7, Use the properties…

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Q: E(Y) –> P(Y > n).

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Q: Suppose that X and Y are random variables. If we know that V(X)=11 and Y=2X−4, determine σ(Y).

A: Given : V(X)=11 and Y=2X−4 V(Y) = V(2X−4) = 22V(X) = 4*11 = 44

Q: Let X - Po(A), A > 0. Determine the PMF of the random variable Y = X² – 3 and

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A: Answer: For the given data,

Q: Let X, and X, be independent random variables. Suppose the mean of X, and X2 are 5 and 2; and…

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Q: 0, x <0, The CDF of the random variable X is F(x)= x²(9-2x) OSx<3, 27 1, 3<X. Calculate P(1 <X<2).

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Q: Let X and Y be two random variable with E(X) = 1,Var(X) = 2, E(Y) = 2,Var(Y) = 2. Then Cov(X –…

A: GivenE(x)=1Var(x)=2E(y)=2Var(y)=2

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A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

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Q: Let X1 ~ x² (n, 8) and X2 ~ x² (m, 2) : mX1 find the expected value of X = nX2 Е (X).

A: We have given two chi square distribution and we have to find the mean of  resultant F distribution.

Q: Suppose that X1, X2, X3, .., X99, X100 are independent Bernoulli(1/2) random variables. What is…

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Q: Let X and Y be two discrete random variables with the following joint probabile function x--1 1 2,…

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Q: Let X ~ U(a,b). Use the definition of the mean of a continuous random variable to show that μX =…

A: The mean of the uniform continuous random variable can be calculated as:

Q: Suppose the p.d.f. of random variable X is defined as x³/20 if1<x< 3 f(x) = otherwise

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Q: Let X, X,...X, be 'n' random variable which are identically distributed such that Xg= 1 with a prob.…

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Q: Suppose that the random variables X and Y are independent with Var(X)=8 and Var(Y)=6. Calculate…

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Q: If x is functionally related to A and B as x = A + B, and if A and B are random variables, then x is…

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Q: Let X and Y are independent uniform random variables supported on [0, 1]. Find the proba- bility…

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Q: We have two independent random variables X, and X2. Let X,~N(5,15) and X2~x?. Calculate P(X, – 5 >…

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Q: If X1 and X2 are independent random variables with distribution given by P[Xi] = −1 = P[Xi = 1] =…

A: Construct the PMF of X1X2, So, P(X1X2 = x) = P(X1=1, X2 = 1) +P(X1=-1, X2 = -1)    if x =1P(X1=-1,…

Q: Let V=X+Y and U=X-Y are random variables, then the condition which make the covariance

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Q: Prove that if X and Y are non-negative independent random variables, then X21Y².

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Q: Suppose that X1, X2, X3, ..., X99, X100 are independent Bernoulli(1/2) random variables. What is…

A: Given: X1, X2, X3, ..., X99, X100 are independent Bernoulli(1/2) random variables. To Find:…

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A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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Q: Two random variables Z and W are defined as Z = X + aY and W = X - aY, where X and Y are also random…

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Q: Let X € {0,1} and Y € {0, 1} be two independent binary random variables. If P(X = 0) = 0.2 and P(Y =…

A: Given that P(X = 0) = 0.2, then P(X = 1) = 1 - 0.2 = 0.8 P(Y = 0) = 0.8, then P(Y = 1) = 1 - 0.8 =…

Q: Suppose that X₁, X₂, X3 are mutually independent random variables with the respective generating…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

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A: To prove that ∑i=0ne-λλxx!=1n!∫λ∞e-xxn   Let take RHS 1n!∫λ∞e-xxn Consider the incomplete gamma…

Q: Suppose that X1,., Xn are iid random variables with 2 P(X; = 0) P(X; = 1) : 3 P(X; = 2) (1 – 0) %3D…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

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Q: 2. Let X be a uniform random variable on [a, 0] and let P(X ≤ -1) = . Then AP[X = -1] = BV[X]=-1/2…

A: Sol

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A: X1,X2,X3 are independent binomial distribution with n = 100, p = 0.2 So,  E(Xi) = np = 100*0.2 = 20…

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Q: .If a random variable X assumes the values 0 and 1 with P(X = 0) = 3 P(X = 1), then compute the…

A: From the given information, P(X=0)=3P(X=1) P(X=0)+P(X=1)=13P(X=1)+P(X=1)=1…

Q: Let Y 0.5X + N, where X and N are independent, zero-mean random variables with %3D o3 = 3.6, af =…

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Q: Show that two random variables X, and X, with joint pdf, 1 |x, < 4, 2<x, <4 fx,„x, (x,x2) ={ 16…

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