Free Printable SL-Section 4

1.

Which properties must a Sigma-Algebra $F$ fulfill?

a)

$\Omega\in F$

b)

$A\in F\ \rightarrow\ \overline{A}\in F$

c)

$A_1,\ldots,A_n\in F\ \rightarrow\$
$A_1\cup\cdots\cup A_n\in F$

d)

$F\subseteq2^{\Omega}$

2.

Mark possible definitions of probability measures on a continuous probability space?

a)

$P\ :\ 2^{\Omega}\ \rightarrow\ \left[0,\ 1\right]$

b)

$P\ :\ 2^{\Omega}\ \rightarrow\ \left(0,\ 1\right)$

c)

$P\ :\ F\ \rightarrow\ \left[0,\ 1\right]$

d)

$P\ :\ F\ \rightarrow\ \left(0,\ 1\right)$

3.

How is the sigma-algebra-generating function $\sigma$ defined?
$\left(\epsilon\subseteq2^{\Omega}\right)$

a)

$\sigma\left(\epsilon\right)\ :=\ \cap\left\{F\ni\epsilon\ :\ F\ is\ \sigma-A.\right\}$

b)

$\sigma\left(\epsilon\right)\ :=\ \cup\left\{F\ni\epsilon\ :\ F\ is\ \sigma-A.\right\}$

4.

Is $\left\{\Omega,\ \left\{\right\}\right\}$ a sigma algebra?

a)

Yes

b)

No

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