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Juliette [100K]
4 years ago
10

The time between requests to a web server is exponentially distributed with mean 0.5 seconds. NOTE: This is a multi-part questio

n. Once an answer is submitted, you will be unable to return to this part. Find the probability that the time between requests is between 1 and 2 seconds. Probabili
Mathematics
1 answer:
lana66690 [7]4 years ago
3 0

Answer:

11.7% probability that the time between requests is between 1 and 2 seconds.

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

f(x) = \mu e^{-\mu x}

In which \mu = \frac{1}{m} is the decay parameter.

The probability that x is lower or equal to a is given by:

P(X \leq x) = \int\limits^a_0 {f(x)} \, dx

Which has the following solution:

P(X \leq x) = 1 - e^{-\mu x}

In this problem, we have that:

m = 0.5, \mu = \frac{1}{m} = 2

Find the probability that the time between requests is between 1 and 2 seconds.

P(1 \leq X \leq 2) = P(X \leq 2) - P(X \leq 1)

P(X \leq 2) = 1 - e^{-2*2} = 0.9817

P(X \leq 1) = 1 - e^{-2*1} = 0.8647

P(1 \leq X \leq 2) = P(X \leq 2) - P(X \leq 1) = 0.9817 - 0.8647 = 0.117

11.7% probability that the time between requests is between 1 and 2 seconds.

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1 1/5 or 6/5

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3 years ago
How to find the area of a sector with a sector angle of 72 degrees and a radius of 14 cm​
skad [1K]

Answer:

Exact area: 39.2π cm²

Approximate area: 123.2 cm²

Step-by-step explanation:

The area of a circle is πr².

A full circle can be thought of as a sector of a circle with 360° of central angle. For a sector of a circle with a central angle of n°, multiply the area of the circle by the fraction n°/360°.

The formula for the area of a sector of circle with central angle n° and radius r is

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Here we have n = 72; r = 14 cm

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A = (72°)/(360°) × π × (14 cm)²

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7 0
1 year ago
Jada made 6 cups of blueberry jam and divided the Jam in 4 containers. How much jam went in each container
Blizzard [7]

1\frac{1}{2} cups of blueberry jam went in each container.

Step-by-step explanation:

Given,

Jada made blueberry jam = 6 cups

Number of containers = 4 containers

Jam in one container = \frac{Cups\ of\ blurberry\ jam\ made}{Number\ of\ containers}

Jam in one container = \frac{6}{4}

Jam in one container = \frac{3}{2} = 1\frac{1}{2}

1\frac{1}{2} cups of blueberry jam went in each container.

Keywords: fractions, division

Learn more about fractions at:

  • brainly.com/question/2013970
  • brainly.com/question/1998796

#LearnwithBrainly

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