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Lesson Example Discussion Quiz: Class Homework

Step-5

Title: Continuous random variable

Grade: 9-a Lesson: S4-L7

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

$5$

Step	Type	Explanation	Answer
1	Problem	A commuter train arrives punctually at a station every 25 minutes. Each morning, a commuter leaves his house and casually walks to the train station. Let X denote the amount of time, in minutes, that commuter waits for the train from the time he reaches the train station. It is known that the probability density function of X is f(x) = \$1/25\$,for 0<x<25 Obtain and interpret the expected value of the random variable X.
2	Formula:	E(X) = \$\int_-\infty^\infty\$x f(x)dx
3	Step	Substitute f(x) in the formula	E(X) = \$\int_0^25 x 1/25\$ dx
4	Step	Simplification	E(X) = \$1/25 \int_0^25 x dx\$
5	Step	Simplification	E(X) = \$1/25 (x^2/2)_0^25\$
6	Step	Simplification	\$E(X) = 1/25 ((25-0)^2)/2\$
7	Step	Simplification	\$E(X) = 1/25 (625/2)\$
8	Step	Simplification	\$E(X) = 625/50\$
9	Step	After simplification	\$12.5\$
10		Answer	C

Step

Type

Explanation

Answer

Problem

A commuter train arrives punctually at a station every 25 minutes. Each morning, a commuter leaves his house and casually walks to the train station. Let X denote the amount of time, in minutes, that commuter waits for the train from the time he reaches the train station. It is known that the probability density function of X is
f(x) = \$1/25\$,for 0<x<25
Obtain and interpret the expected value of the random variable X.

Formula:

E(X) = \$\int_-\infty^\infty\$x f(x)dx

Step

Substitute f(x) in the formula

E(X) = \$\int_0^25 x 1/25\$ dx

Step

Simplification

E(X) = \$1/25 \int_0^25 x dx\$

Step

Simplification

E(X) = \$1/25 (x^2/2)_0^25\$

Step

Simplification

\$E(X) = 1/25 ((25-0)^2)/2\$

Step

Simplification

\$E(X) = 1/25 (625/2)\$

Step

Simplification

\$E(X) = 625/50\$

Step

After simplification

\$12.5\$

Answer

Tutor: Questions

Seq	Type	Question
1	Problem	What did you learn from this problem?
2	Clue	What did you learn from the clues?
3	Hint	What did you learn from the Hints?
4	Step	What did you learn from the Steps?
5	Step	How can we improve the Steps?

Seq

Type

Question

Audio

Problem

What did you learn from this problem?

Clue

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Hint

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Step

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Step

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