Random Variable Flashcards
How do you find probability in random variable (both DRV and CRV)
In DRV, we find prob through Probability Mass Function : f(xₖ) = P(X=Xₖ) [for every x, we find probability]
In CRV, prob through Probability Mass Function : P(X=Xₖ) = 0 [Probability at point=0]
Therefore in CRV, we find prob through Probability density function(Area under curve): f(x) is p.d.f iff ∫f(x) dx = 1 (from -∞ to ∞ integration limits)
Probability mass function (DRV)
Probability Mass Function: f(xₖ) = P(X=Xₖ) [for every x, we find probability]
Probability mass function (CRV)
Probability Mass Function : P(X=Xₖ) = 0 [Probability at point=0]
Probability Density Function (DRV)
NOT GIVEN
Probability Density Function (CRV)
Probability density function: Probability given by area under P.D.F
f(x) is valid P.D.F iff ∫f(x) dx = 1 (from -∞ to ∞ integration limits) {Area under curve}
Cumulative distribution function (DRV)
Cumulative distribution function (CRV)
Expectation of X (DRV and CRV)
Variance(X) (3formula) (also definitions) (Also notation)
Range of variance
Var(x)>=0
E(x²)
Difference between E(x²) and (E(x))²
Standard deviation (notation, formula, range)
When will be var(x) = 0
Var(x) = 0 only when x=constant=x̄ (here x is called invariant)
Importance of Expectation in game
Importance of standard deviation in real life
Property 1 of mean, variance and standard deviation
Property 2 of mean, variance and standard deviation
Property 3 of mean, variance and standard deviation
Property 4 of mean, variance and standard deviation
Property 5 of mean, variance and standard deviation
Property 6 of mean, variance and standard deviation
Property 7 of mean, variance and standard deviation
Covariance(X,Y)
If X,Y are independent random variable then
