Prove Var(|X|) <= Var(X)

Expert Solution

TOPIC:Inequality based on Variance.

milcah answered 1 year ago

Show that Var(x-a/)=1/h^2 Var(x)

QUESTION 1 Consider the following program: var x = 0; function sub1() { var x =...

QUESTION 1 Consider the following program: var x = 0; function sub1() { var x = 1; function sub2() { function sub3() { print x; } sub3(); } function sub4() { var x = 2; sub2(); } sub4(); } sub1(); If this code uses static scoping, when it is executed what is printed? 0 1 2 QUESTION 2 Consider the following program: var x = 0; function sub1() { var x = 1; function sub2() { function sub3() { print...

E(Y) = 4, E(X) = E(Y+2), Var(X) = 5, Var(Y) = Var(2X+2) a. What is E(2X...

E(Y) = 4, E(X) = E(Y+2), Var(X) = 5, Var(Y) = Var(2X+2) a. What is E(2X -2Y)? b. What is Var(2X-Y+2)? c. What is SD(3Y-3X)? 2) In a large community, 65% of the residents want to host an autumn community fair. The rest of the residents answer either disagree or no opinion on this proposal. A sample of 18 residents was randomly chosen and asked for their opinions. a) What is th probability that the residents answer either disagree or...

X ∼ NBD(r, p). Derive the var(X).

Given: E[x] = 4, E[y] = 6, Var(x) = 2, Var(y) = 1, and cov(x,y) =...

Given: E[x] = 4, E[y] = 6, Var(x) = 2, Var(y) = 1, and cov(x,y) = 0.2 Find a lower bound on (5 < x + y < 10). State the theorem used.

If Var(X) = 1, Var(Y) = 2 and Cov(X,Y) = 0, what is Cov(X-2Y, Y-X2)?

2. Numerical “Proof” that for X,Y independent,Var(X+Y) = Var(X−Y) =σ2X+σ2Y: 2.1 As we did in Lab...

2. Numerical “Proof” that for X,Y independent,Var(X+Y) = Var(X−Y) =σ2X+σ2Y: 2.1 As we did in Lab 4, you will need to generate a sample(x,y)-values by independently generating x-values and y-values.(You may choose sample size of 50000.) State the two distributions you will use for generating x-values and y-values,and the corresponding population variances. 2.2 Compute the sample variances of the (X+Y)-values, and of the (X−Y)-values. What value are these two sample variances supposed to estimate? 2.3 Use the formula that explains...

Prove the Following: Where a and b are constants. a). Σ(?−?̅)=0 b). Var( a + bX)...

Prove the Following: Where a and b are constants. a). Σ(?−?̅)=0 b). Var( a + bX) = b2Var(X)

Suppose that x is real number. Prove that x+1/x =2 if and only if x=1. Prove...

Suppose that x is real number. Prove that x+1/x =2 if and only if x=1. Prove that there does not exist a smallest positive real number. Is the result still true if we replace ”real number” with ”integer”? Suppose that x is a real number. Use either proof by contrapositive or proof by contradiction to show that x3 + 5x = 0 implies that x = 0.

2. Prove the following properties. (b) Prove that x + ¯ xy = x + y.

2. Prove the following properties.(b) Prove that x + ¯ xy = x + y.3. Consider the following Boolean function: F = x¯ y + xy¯ z + xyz(a) Draw a circuit diagram to obtain the output F. (b) Use the Boolean algebra theorems to simplify the output function F into the minimum number of input literals.

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