The expected value E ( X ) and interpret it, whenrandom variable X denotes the useful life (in hundreds of hours) of a certain machine component with thecumulative distribution functionis F ( x ) = 1 9 x 2 , 0 ≤ x ≤ 3 .

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Answer 1

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Chapter 12.3, Problem 11E

(a)

To determine

To calculate: The expected value E(X) and interpret it, whenrandom variable X denotes the useful life (in hundreds of hours) of a certain machine component with thecumulative distribution functionis F(x)=19 x2, 0≤x≤3.

(b)

To determine

To calculate: The variance Var(X), when a random variable X denotes the useful life (in hundreds of hours) of a certain machine component with the cumulative distribution function F(x)=19 x2, 0≤x≤3.

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Use a graph of f to estimate lim f(x) or to show that the limit does not exist. Evaluate f(x) near x = a to support your conjecture. Complete parts (a) and (b). x-a f(x)= 1 - cos (4x-4) 3(x-1)² ; a = 1 a. Use a graphing utility to graph f. Select the correct graph below.. A. W → ✓ Each graph is displayed in a [- 1,3] by [0,5] window. B. in ✓ ○ C. und ☑ Use the graphing utility to estimate lim f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. x-1 ○ A. The limit appears to be approximately ☐ . (Round to the nearest tenth as needed.) B. The limit does not exist. b. Evaluate f(x) for values of x near 1 to support your conjecture. X 0.9 0.99 0.999 1.001 1.01 1.1 f(x) ○ D. + ☑ (Round to six decimal places as needed.) Does the table from the previous step support your conjecture? A. No, it does not. The function f(x) approaches a different value in the table of values than in the graph, after the approached values are rounded to the…

x²-19x+90 Let f(x) = . Complete parts (a) through (c) below. x-a a. For what values of a, if any, does lim f(x) equal a finite number? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. x→a+ ○ A. a= (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no values of a for which the limit equals a finite number. b. For what values of a, if any, does lim f(x) = ∞o? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. x→a+ A. (Type integers or simplified fractions) C. There are no values of a that satisfy lim f(x) = ∞. + x-a c. For what values of a, if any, does lim f(x) = -∞0? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. x→a+ A. Either a (Type integers or simplified fractions) B.

Sketch a possible graph of a function f, together with vertical asymptotes, that satisfies all of the following conditions. f(2)=0 f(4) is undefined lim f(x)=1 X-6 lim f(x) = -∞ x-0+ lim f(x) = ∞ lim f(x) = ∞ x-4 _8

Answer 2

Question

Chapter 12.3, Problem 11E

(a)

To determine

To calculate: The expected value E(X) and interpret it, whenrandom variable X denotes the useful life (in hundreds of hours) of a certain machine component with thecumulative distribution functionis F(x)=19 x2, 0≤x≤3.

(b)

To determine

To calculate: The variance Var(X), when a random variable X denotes the useful life (in hundreds of hours) of a certain machine component with the cumulative distribution function F(x)=19 x2, 0≤x≤3.

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Answer 3

Question

Chapter 12.3, Problem 11E

(a)

To determine

To calculate: The expected value E(X) and interpret it, whenrandom variable X denotes the useful life (in hundreds of hours) of a certain machine component with thecumulative distribution functionis F(x)=19 x2, 0≤x≤3.

(b)

To determine

To calculate: The variance Var(X), when a random variable X denotes the useful life (in hundreds of hours) of a certain machine component with the cumulative distribution function F(x)=19 x2, 0≤x≤3.

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Answer 4

Question

Chapter 12.3, Problem 11E

(a)

To determine

To calculate: The expected value E(X) and interpret it, whenrandom variable X denotes the useful life (in hundreds of hours) of a certain machine component with thecumulative distribution functionis F(x)=19 x2, 0≤x≤3.

(b)

To determine

To calculate: The variance Var(X), when a random variable X denotes the useful life (in hundreds of hours) of a certain machine component with the cumulative distribution function F(x)=19 x2, 0≤x≤3.

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Answer 5

Chapter 12.3, Problem 11E

(a)

To determine

To calculate: The expected value E(X) and interpret it, whenrandom variable X denotes the useful life (in hundreds of hours) of a certain machine component with thecumulative distribution functionis F(x)=19 x2, 0≤x≤3.

(b)

To determine

To calculate: The variance Var(X), when a random variable X denotes the useful life (in hundreds of hours) of a certain machine component with the cumulative distribution function F(x)=19 x2, 0≤x≤3.

Answer 6

Chapter 12.3, Problem 11E

(a)

To determine

To calculate: The expected value E(X) and interpret it, whenrandom variable X denotes the useful life (in hundreds of hours) of a certain machine component with thecumulative distribution functionis F(x)=19 x2, 0≤x≤3.

Answer 7

Chapter 12.3, Problem 11E

(a)

To determine

To calculate: The expected value E(X) and interpret it, whenrandom variable X denotes the useful life (in hundreds of hours) of a certain machine component with thecumulative distribution functionis F(x)=19 x2, 0≤x≤3.

Answer 8

(b)

To determine

To calculate: The variance Var(X), when a random variable X denotes the useful life (in hundreds of hours) of a certain machine component with the cumulative distribution function F(x)=19 x2, 0≤x≤3.

Answer 9

(b)

To determine

To calculate: The variance Var(X), when a random variable X denotes the useful life (in hundreds of hours) of a certain machine component with the cumulative distribution function F(x)=19 x2, 0≤x≤3.

Answer 10

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Answer 11

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Answer 12

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Answer 13

Ch. 12.1 - Compute the expected value and the variance of the...Ch. 12.1 - Prob. 2CYU Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Probability Table, Expected Value The number of...Ch. 12.1 - Prob. 7E Ch. 12.1 - Prob. 8E

The expected value E ( X ) and interpret it, whenrandom variable X denotes the useful life (in hundreds of hours) of a certain machine component with thecumulative distribution functionis F ( x ) = 1 9 x 2 , 0 ≤ x ≤ 3 .

Solution Summary: The author calculates the expected value E(X)=2 and interprets it.

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To calculate: The expected value E(X) and interpret it, whenrandom variable X denotes the useful life (in hundreds of hours) of a certain machine component with thecumulative distribution functionis F(x)=19 x2, 0≤x≤3.

To calculate: The variance Var(X), when a random variable X denotes the useful life (in hundreds of hours) of a certain machine component with the cumulative distribution function F(x)=19 x2, 0≤x≤3.

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