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asambeis [7]
3 years ago
12

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 p

(x) 5 5 1yn x 5 1, 2, 3,…, n 0 otherwise (this is called the discrete uniform distribution). Compute E(X) and V(X) using the shortcut formula. [Hint: The sum of the first n positive integers is n(n 1 1)y2, whereas the sum of their squares is n(n 1 1)(2n 1 1)y6.]
Mathematics
1 answer:
Anon25 [30]3 years ago
3 0

Answer:

A. E(x) = 1/n×n(n+1)/2

B. E(x²) = 1/n

Step-by-step explanation:

The n candidates for a job have been ranked 1,2,3....n. Let x be the rank of a randomly selected candidate. Therefore, the PMF of X is given as

P(x) = {1/n, x = 1,2...n}

Therefore,

Expectation of X

E(x) = summation {xP(×)}

= summation {X×1/n}

= 1/n summation{x}

= 1/n×n(n+1)/2

= n+1/2

Thus, E(x) = 1/n×n(n+1)/2

Value of E(x²)

E(x²) = summation {x²P(×)}

= summation{x²×1/n}

= 1/n

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Answer:

The length of the base is 11 meters.

Step-by-step explanation:

The diagram of the triangle is not shown; However, the given details are enough to solve this question.

Given

<em>Shape: Triangle</em>

<em>Represent the height with h and the base with b</em>

b = 3 + 2h

Area = 22

Required

Find the length of the base

The area of a triangle is calculated as thus;

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Substitute 22 for Area and 3 + 2h for b

The formula becomes

22 = \frac{1}{2} * (3 + 2h) * h

Multiply both sides by 2

2 * 22 = 2 * \frac{1}{2} * (3 + 2h) * h

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Open the bracket

44 = 3 * h + 2h * h

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Subtract 44 from both sides

44 - 44 = 3h + 2h^2 - 44

0 = 3h + 2h^2 - 44

Rearrange

0 = 2h^2 +3h - 44

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At this point, we have a quadratic equation; which is solved as follows:

2h^2 +3h - 44 = 0

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Solve the above linear equations separately

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Add 4 to both sides

h - 4 + 4 = 0 + 4

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2h + 11 = 0

Subtract 11 from both sides

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Divide both sides by 2

\frac{2h}{2} = -\frac{11}{2}

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Since height can be negative, we'll discard h = -\frac{11}{2}

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Recall that b = 3 + 2h

Substitute 4 for h

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Hence, the length of the base is 11 meters

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Answers:
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