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Aim

Prelims

Theory

Pretest

Procedure

Experiments

Posttest

References

Contributors

Feedback

Random Variables

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Beginner

Intermediate

Advanced

1. Given two sets

F = \{1, 4, 6, 7 \}

and

E = \{0, 1, 2 \}

what is

E \oplus F

a:

\{1, 2, 7\}

Explanation

Explanation

b:

\{1, 6, 7\}

Explanation

Explanation

c:

\{0, 4, 6, 7\}

Explanation

Explanation

d:

\{6, 7\}

Explanation

Explanation

2. For a sample space

\Omega = \{a,b,c,d\}

a collection

C = \{ \phi, \Omega, \{a\}, \{b,c,d\}, \{b, c\}, \{a, b\}, \{a, d\}, \{ d\}, \{a, b, c\} \}

there is one subset which has to be removed from

C

such that

C

becomes a sigma alebra. Which one is it?

a:

\{a\}

Explanation

Explanation

b:

\{a, b \}

Explanation

Explanation

c:

\{b, c, d\}

Explanation

Explanation

d:

\{b, c\}

Explanation

Explanation

3. For a sample space

\Omega = \{w_1,w_2, w_3\}

, and a random variable

X

such that

X(w_1) = -2.5

,

X(w_2) = 3

and inverse images

X^{-1}(3.5) = \{w_1, w_2, w_3\}

and

X^{-1}(0) = \{ w_1\}

, what can be the range for the value of

mathcal{X}(w_3)

?

a:

-\infty

to

0

Explanation

Explanation

b:

-\infty

to

-2.5

Explanation

Explanation

c:

0.5

to

3.5

Explanation

Explanation

d: None of the above Explanation

Explanation

4. Given a

\Omega = \{1, 2, 3, 4\}

and

\mathcal{F} = \{ \phi, \Omega, \{1\}, \{2\}, \{1,2\}, \{3,4\}, \{1,3,4\}, \{2,3,4\}\}

which of the following is a valid random variable mapping

a:

X(1) = 1, X(2) = 2, X(3) = 3, X(4) = 4

Explanation

Explanation

b:

X(1) = 1, X(2) = 2, X(3) = 3, X(4) = 3

Explanation

Explanation

c:

X(1) = 5, X(2) = 4, X(3) = 1, X(4) = 0

Explanation

Explanation

d:

X(1) = 6, X(2) = 1, X(3) = 2, X(4) = 8

Explanation

Explanation

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