ISYE 6644 Midterm 3 Cheat Sheet: Key Concepts and Formulas Latest Update with complete sol

ISYE 6644 Midterm 3 Cheat Sheet: Key Concepts and Formulas
IYSE 6644 Midterm 3 Cheat Sheet



Σ ´
E[X]Discrete
= x xf (x) E[X]Continuous
= R xf (x)dx
0 Σ ´
E[h(X)] = x h(x)f (x) E[h(X)] = R h(x)f (x)dx
nth moment of X: E[Xn]
sin(x) nth central moment of X: E[(X − E[X]n]
cos(x) Variance of X: E[(X − E[X]2] = E[X2] − (E[X])2
√
Standard Deviation of X: Var(X) successes.
E[aX+b]: aE[X] + b Var(aX+b): a2Var(X)
Moment-generating function: MX (t) = E[etX ]
Generating Moments: E[Xk] = dk/dtkMx(t)|t=0




Number of Bernoulli(p) trials for r successes.

´ ´ ´
´ ´

, D