Suppose the random varaible Y has non-zero probability at 0,1,2,3,... (i.e. the support of Y is the set of non-negative integers).(adsbygoogle = window.adsbygoogle || []).push({});

Define a random variable W:

W=0 ,if Y=0,1,2,or 3

--=Y-3 ,if Y=4,5,...

Define a random variable Z:

Z=max{0,Y-3}=0 ,if Y≦3

--------------=Y-3 ,if Y>3

And I have 2 questions...

1) Can I say that W and Z areequal as random variables(i.e. W=Z) ?

(what is bothering me is that W is undefined at e.g. Y=0.5, Y=2.2, etc. while Z is defined everywhere, my notes say that W and Z are equal random varaibles, but I just struggle to understand why)

2) Is it true that E(W)=E(Z) ?

Hopefully someone can clarify this! Thank you!

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Equality of random variables

Loading...

Similar Threads - Equality random variables | Date |
---|---|

I Equality in conditional probability | Jan 18, 2018 |

I Rewriting of equality in conditional probability distribution | Jan 16, 2018 |

I How to choose the largest reward but to be shared equally among the people choosing it | Oct 23, 2017 |

Almost equal random variables | Aug 4, 2009 |

**Physics Forums - The Fusion of Science and Community**