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4 years ago

What do you mean by the term standard unit ?

Mathematics

2 answers:

ira [324]4 years ago

4 0

Answer:

When numbers become very small or large standard form (or standard index form) is used to make them manageable. In standard form or unit a number is written as:

[a number between 1 and 10] × [ an integer power of 10]

IRINA_888 [86]4 years ago

3 0

A standard unit of measurement is a quantifiable language that helps everyone understand the association of the object with the measurement. It is expressed in inches, feet, and pounds, in the United States, and centimeters, meters, and kilograms in the metric system.

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The n candidates for a job have been ranked 1, 2, 3,..., n. Let X 5 the rank of a randomly selected candidate, so that X has pmf

jeka57 [31]

Question:

The n candidates for a job have been ranked 1, 2, 3,..., n. Let x = rank of a randomly selected candidate, so that x has pmf:

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(this is called the discrete uniform distribution).

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Answer:

$E(x) = \frac{n+1}{2}$

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Step-by-step explanation:

Given

PMF

$p(x) = \left \{ {{\frac{1}{n}\ \ x=1,2,3...,n} \atop {0\ \ \ Otherwise}} \right.$

Required

Determine the E(x) and Var(x)

E(x) is calculated as:

$E(x) = \sum \limits^{n}_{i} \ x * p(x)$

This gives:

$E(x) = \sum \limits^{n}_{x=1} \ x * \frac{1}{n}$

$E(x) = \sum \limits^{n}_{x=1} \frac{x}{n}$

$E(x) = \frac{1}{n}\sum \limits^{n}_{x=1} x$

From the hint given:

$\sum \limits^{n}_{x=1} x =\frac{n(n +1)}{2}$

So:

$E(x) = \frac{1}{n} * \frac{n(n+1)}{2}$

$E(x) = \frac{n+1}{2}$

Var(x) is calculated as:

$Var(x) = E(x^2) - (E(x))^2$

Calculating: $E(x^2)$

$E(x^2) = \sum \limits^{n}_{x=1} \ x^2 * \frac{1}{n}$

$E(x^2) = \frac{1}{n}\sum \limits^{n}_{x=1} \ x^2$

Using the hint given:

$\sum \limits^{n}_{x=1} \ x^2 = \frac{n(n +1)(2n+1)}{6}$

So:

$E(x^2) = \frac{1}{n} * \frac{n(n +1)(2n+1)}{6}$

$E(x^2) = \frac{(n +1)(2n+1)}{6}$

So:

$Var(x) = E(x^2) - (E(x))^2$

$Var(x) = \frac{(n+1)(2n+1)}{6} - (\frac{n+1}{2})^2$

$Var(x) = \frac{(n+1)(2n+1)}{6} - \frac{n^2+2n+1}{4}$

$Var(x) = \frac{2n^2 +n+2n+1}{6} - \frac{n^2+2n+1}{4}$

$Var(x) = \frac{2n^2 +3n+1}{6} - \frac{n^2+2n+1}{4}$

Take LCM

$Var(x) = \frac{4n^2 +6n+2 - 3n^2 - 6n - 3}{12}$

$Var(x) = \frac{4n^2 - 3n^2+6n- 6n +2 - 3}{12}$

$Var(x) = \frac{n^2 -1}{12}$

Apply difference of two squares

$Var(x) = \frac{(n+1)(n-1)}{12}$

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3 years ago

Solve the simultaneous equations:<br> 3x + 2y = 35 <br> 2x + 3y = 30

lesya [120]

Answer:

nuber 1

Simplifying

3x + 2y = 35

Solving

3x + 2y = 35

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2y' to each side of the equation.

3x + 2y + -2y = 35 + -2y

Combine like terms: 2y + -2y = 0

3x + 0 = 35 + -2y

3x = 35 + -2y

Divide each side by '3'.

x = 11.66666667 + -0.6666666667y

Simplifying

x = 11.66666667 + -0.6666666667y

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3 years ago

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The correct answer is D

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3 years ago

What do you mean by the term standard unit ?​

What do you mean by the term standard unit ?