Find E (X) and E(X²) and using these values evaluate E[(2X + 1)²]

Q: Given f(x) = 2x- 4 and g(x) = x - 1, on which interval are both functions negative?

A: I am going to solve the problem by using some simple algebra to get the required result of the given…

Q: f(x) = x2 −2x + 1; g(x) = x −1. f(x) = log2 x; g(x) = 2x. f(x) = ⌊ x ⌋; g (x) = ⌈ x ⌉, f(x) =…

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Q: log(2-1)(3+ j√3)

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Q: Find E(X) X  0 1 2 3 P(X) 0.2 0.4 0.2 0.2 Use Excel

A: The probability distribution is: X P(X) 0 0.2 1 0.4 2 0.2 3 0.2

Q: In each case, select the function that dominates the other as x → ∞o? (a) O 50x² (b) 0.02x³ O In(x +…

A: limx→∞0.02x350x2=limx→∞0.02x50=∞    Therefore, 0.02x3, will dominates over 50x2

Q: Let f(x) = log, (x). %3D Select all the correct g(x) functions such that f (x) is O(g(x)). g(x) = x

A: These problems following by carefully applying the definition of the Big O notation. The typeset…

Q: Find a number x such that x + 1 / x − 2 = 3x

A: The expression could be x+1x-2=3x or x+1x-2=3x. If the expression is x+1x-2=3x, then…

Q: If E[X] = −3 and Var(X) = 5, then E[(5 + 6X)²] = and Var(3 + 5X) =

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Q: Let X1, X2, X3 and X4 be a random sample from population with pdf X, 0 < x < 1 fx(x) = |0,…

A: Given information: The probability distribution function is fXx=x,    0&lt;x&lt;10,    otherwise.

Q: Use f(x) = log4(16x) and g(x) = 4* to answer the questions below. (a) Find f(g(x)) and simplify. x+2…

A: Given query is to perform indicated function operations.

Q: Differentiate the function y = In [(x* – 1)(x² + 1)²] to the simplest form. - The number of online…

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Q: Let X be a random variable from the Pareto distribution with probability density function {(=10) = {…

A: Solution

Q: Let f(x)=x³ and g(x)=Jx, and h(x)=–. Find each of the following: 3 g(h(f(x))) g(h(f(x))) =

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Q: If E[X] = 5 and Var(X) = 4, then E[(4 + 5X)²] = [] and Var(3+5X) 0

A: Given that :E(X)= 5 and Var( X )=4 .For a random variable X…

Q: If E[X 4 and Var(X) 1, then E(1 + 5X)²] - and Var(2 + 4X)

A: GivenE(X)=4Var(X)=1

Q: What happens to this base function and why? a(x)= x2

A: The function a(x)=x2 is a basic quadratic function. In this function:- x is the input variable.- x2…

Q: For f(x)=4xand g(x)=x+5 find the following. a.(f◦g)(x)                            b.(g◦f)(x)…

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Q: [cx)= (x+1) 「cx)-(x_)[cxー1) (xー1)「cx-1) [(-x)= [(1-x) |

A: Γ(x)=∫0∞tx-1e-tdt  for x&gt;0Γ(x+1)=∫0∞txe-tdt =-txe-t0∞+x∫0∞tx-1e-tdt=xΓ(x)⇒Γ(x)=Γ(x+1)x Now,…

Q: d. Compute E(X) and Var(X).

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Q: Show that E( X - K )2 = var( X) + [E(X) - K]2

A: var(X)=E(X2)-E(X)2 E(a)=a  where a is constant (a-b)2=a2-2ab+b2