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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 the 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 characterizes how likely it is for that variable to take a 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 the 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


        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

January 5, 2021

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