Question

Give a practical example of a probability space and show that it satisfies the three properties of a probability space.

Answer 1

probability space is a measure space such that the measure of the whole space is equal to one.

A probability space is a triple ( Ω , F , P ).:

If the experiment consists of just one flip of a fair coin, then the outcome is either heads or tails: Ω = { H , T } . The σ-algebra F = 2 ^Ω contains 2 ^2 = 4 events, namely: { H } (“heads”), { T } (“tails”), (“neither heads nor tails”), and { H , T }, (“either heads or tails”); in other words, F = { { } , { H } , { T } , { H , T } } . There is a fifty percent chance of tossing heads and fifty percent for tails, so the probability measure in this example is P ( { } ) = 0 , P ( { H } ) = 0.5 , P ( { T } ) = 0.5, P ( { H , T } ) = 1.

As we can see by this example of fliping a coin, three properties of probability space satisfies.