Random Process & Random Variable

Random Process – an event or experiment that has a random outcome. Something that you can’t predict accurately. Might know the range of possibilities.

e.g. flipping a coin, rolling a die or playing on a slot machine.

Random Variable (X)

In statistics, a random variable takes random values such as weight of the next person entering the class or what number comes when we throw a die. For a random variable X, we would like to know the values it can take or more interested in to characterizes how likely it is for that variable to take particular value x. For example, we are not just interested in knowing the numbers that come up when we throw a die but more interested in how likely it is to get 6 when we throw a die.

Or in a simpler way – A variable whose possible values are a numerical outcome of a random process.

P(X=x) – Probability of variable X taking a value x

1. P – Is the variable’s density function & characterizes variable’s distribution

2. P(X=x) >=0 For any value of x, the probability of X having x can never be less than zero

3. Sum of P(X=x) for all possible values of x is equal to 1

Examples  

        1. Flipping a Coin

Here X= H, T – then the probability of x = H (Head) can never be more than 1. x = H (Head) can never be less than zero. Also, the sum of probabilities of coming Head & Tails is equal to 1

Probability of coming Head – 0.5

Probability of coming Tails – 0.5

Sum of probabilities = P(H) +P(T) = 0.5 + 0.5 = 1

      2. Rolling a Die

X = 1,2,3,4,5,6