- #1

fog37

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- TL;DR Summary
- Difference between random variable and random process

Hello,

When flipping a fair coin 4 times, the two possible outcomes for each flip are either H or T with the same probability ##P(H)=P(T)=0.5##.

Why are the 4 outcomes to be considered as the realizations of 4 different random variables and not as different realizations of the same random variables? A random variable is the outcome (numerical or categorical) of a random experiment. More properly, a random variable is a function that assigns a real number to each outcome of a random experiment.

I guess each coin flip is seen as a separate and independent random experiment so each outcome is therefore associated to different a different random variable...?

A random/stochastic process is generally introduced as a family of time-series where the values of the various time series at the same and specific time instant ##t## are the realization of the SAME random variables...Can a stochastic process be seen as a sequence of random variables and their realizations across different experiments? For example, we can collect the random signal temperature T(t) at 5 different locations to obtain a random process...

Could we define a sequence of coin flips a random process?

Thanks

When flipping a fair coin 4 times, the two possible outcomes for each flip are either H or T with the same probability ##P(H)=P(T)=0.5##.

Why are the 4 outcomes to be considered as the realizations of 4 different random variables and not as different realizations of the same random variables? A random variable is the outcome (numerical or categorical) of a random experiment. More properly, a random variable is a function that assigns a real number to each outcome of a random experiment.

I guess each coin flip is seen as a separate and independent random experiment so each outcome is therefore associated to different a different random variable...?

A random/stochastic process is generally introduced as a family of time-series where the values of the various time series at the same and specific time instant ##t## are the realization of the SAME random variables...Can a stochastic process be seen as a sequence of random variables and their realizations across different experiments? For example, we can collect the random signal temperature T(t) at 5 different locations to obtain a random process...

Could we define a sequence of coin flips a random process?

Thanks