A Random Variable Is A Numerical Measure Of The Outcome From A Probability Experiment 1

Random Variable and Its Probability distribution “A random variable is a variable hat assumes numerical values associated with the random outcome of an experiment, where one (and only one) numerical value is assigned to each sample point”.
“A random variable is a numerical measure of the outcome from a probability experiment, so its value is determined by chance. Random variables are denoted using letters such as X,Y,Z”.
X = number of heads when the experiment is flipping a coin 20 times.
There are two types of random variable
a) Discrete random variable
b) Continuous random variable
A discrete random variable is a random variable that has values that has either a finite number of possible values or a countable number of possible values.
A continuous random variable is a random variable that has an infinite number of possible values that is not countable.
A probability distribution provides the possible values of the random variable and their corresponding probabilities. A probability distribution can be in the form of a table, graph or mathematical formula.
Probabilities, P(x), associated with Discrete random variables have the following properties.
a) p(x) ≥ 0 for all values of x
b) p(x) = 1

EXAMPLE: Identifying Probability Distributions
Is the following a probability distribution?

P(X=x) =P(x) = 0.16 + 0.18 + 0.22 + 0.10 + 0.3 + 0.01 = 0.97 <1 , Not a probability distribution.
EXAMPLE: Identifying Probability Distributions

P(X=x) =P(x) = 0.16 + 0.18 + 0.22 + 0.10 + 0.3 + 0.04 = 1, It is a probability distribution
The mean, or expected value, of a discrete random variable is

The variance of a discrete random variable x is

Laws of Expected Value…”Useful to know”
1. E(c) = c
2. E(X + c) = E(X) + c
3. E(cX) = cE(X)
4. E(X+Y)=E(X)+E(Y)
Laws of Variance…
1. V(c) = 0
2. V(X + c) = V(X)
3. V(cX) = c2V(X)
4. V(X+Y)=V(X)+V(Y)
5. V(X-Y)=V(X)+V(Y)