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Lesson Example Discussion Quiz: Class Homework

Step-3

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

Step	Type	Explanation	Answer
1	Problem	Given P.D.F. of a continuous random variable x as \$f(x) = \begin{cases} x^2/3,for & -1≤x≤2 \\ 0,& otherwise \\ \end{cases}\$.Determine the C.D.F. of x and find P(1<x<2)
2	Step	Finding the C.D.F. of x	f(x) = \$\int_-1^x f(x) dx\$
3	Step	Substitute f(x) in the formula	f(x) = \$\int_-1^x y^2/3 dx\$
4	Step	Simplification	\$f(x) = 1/3 \int_-1^x y^3/3\$ dx
5	Step	Simplification	\$f(x) = (y^3/9)_-1^x\$
6	Step	After simplification	\$f(x)= (x^3+1)/9 ,x∈R\$
7	Step	Finding the value of P(1<x<2)	f(2) - f(1)
8	Step	P(1<x<2)	\$(2^3+1)/9\$ + \$(1^3+1)/9\$
9	Step	P(1<x<2)	\$1 - 2/9 = 7/9\$
10		Answer	B

Step

Type

Explanation

Answer

Problem

Given P.D.F. of a continuous random variable x as
\$f(x) = \begin{cases} x^2/3,for & -1≤x≤2 \\ 0,& otherwise \\ \end{cases}\$.Determine the C.D.F. of x and find P(1<x<2)

Step

Finding the C.D.F. of x

f(x) = \$\int_-1^x f(x) dx\$

Step

Substitute f(x) in the formula

f(x) = \$\int_-1^x y^2/3 dx\$

Step

Simplification

\$f(x) = 1/3 \int_-1^x y^3/3\$ dx

Step

Simplification

\$f(x) = (y^3/9)_-1^x\$

Step

After simplification

\$f(x)= (x^3+1)/9 ,x∈R\$

Step

Finding the value of P(1<x<2)

f(2) - f(1)

Step

P(1<x<2)

\$(2^3+1)/9\$ + \$(1^3+1)/9\$

Step

P(1<x<2)

\$1 - 2/9 = 7/9\$

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

What did you learn from the clues?

Hint

What did you learn from the Hints?

Step

What did you learn from the Steps?

Step

How can we improve the Steps?