Virtual Labs

Tools

Aim

Theory

Pretest

Procedure

Simulation

Posttest

References

Contributors

Feedback

Aim

Theory

Pretest

Procedure

Simulation

Posttest

References

Contributors

Feedback

Functions of a Random Variable

Choose difficulty:

Beginner

Intermediate

Advanced

1.Let

X

be a continuous random variable with PDF

f_X(x) = \left\{ \begin{array}{ll} x^2\left(2x+\frac{3}{2}\right) & \quad 0 < x \leq 1\ 0 & \quad ext{otherwise} \end{array} \right.

a:

\frac{21}{36}

Explanation

Explanation

b:

\frac{61}{36}

Explanation

Explanation

c:

\frac{51}{36}

Explanation

Explanation

d:

\frac{71}{36}

Explanation

Explanation

2. Let

A = XY

denote the area and

L = 2(X + Y)

the length of the perimeter of a rectangle with length

X

and height

Y

, such that

X

and

Y

are independent, and uniformly distributed on the interval

[0, 1]

. Find

E[A]

a: 0.25 Explanation

Explanation

b: 0.5 Explanation

Explanation

c: 0.8 Explanation

Explanation

d: 0.4 Explanation

Explanation

3. Let

A = XY

denote the area and

L = 2(X + Y)

the length of the perimeter of a rectangle with length

X

and height

Y

, such that

X

and

Y

are independent, and uniformly distributed on the interval

[0, 1]

. Find

E[L]

.

a: 0.5 Explanation

Explanation

b: 2 Explanation

Explanation

c: 1 Explanation

Explanation

d: 4 Explanation

Explanation

4. Let

A = XY

denote the area and

L = 2(X + Y)

the length of the perimeter of a rectangle with length

X

and height

Y

, such that

X

and

Y

are independent, and uniformly distributed on the interval

[0, 1]

. Find

Var(A).

a:

\frac{7}{144}

Explanation

Explanation

b:

\frac{27}{144}

Explanation

Explanation

c:

\frac{17}{144}

Explanation

Explanation

d:

\frac{37}{144}

Explanation

Explanation

5. Let

A = XY

denote the area and

L = 2(X + Y)

the length of the perimeter of a rectangle with length

X

and height

Y

, such that

X

and

Y

are independent, and uniformly distributed on the interval

[0, 1]

. Find

Var(L)

.

a:

\frac{1}{4}

Explanation

Explanation

b:

\frac{2}{4}

Explanation

Explanation

c:

\frac{1}{3}

Explanation

Explanation

d:

\frac{2}{3}

Explanation

Explanation

Community Links Sakshat Portal Outreach Portal FAQ: Virtual Labs

Contact Us Phone: General Information: 011-26582050 Email: support@vlabs.ac.in

Follow Us

AGPL 3.0 & Creative Commons (CC BY-NC-SA 4.0)