ISYE 6644 Exam 1 Cheat Sheet (contact: )
Σ
Discrete ´
Continuous
a 0 E[X] = x xf (x) E[X] = R xf (x)dx
Σ ´
E[h(X)] = x h(x)f (x) E[h(X)] = R h(x)f (x)dx
nth moment of X: E[Xn]
nth central moment of X: E[(X − E[X]n]
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.
´ R
arrivals observed between time 0 and time t.
R R
´
Σ
Discrete ´
Continuous
a 0 E[X] = x xf (x) E[X] = R xf (x)dx
Σ ´
E[h(X)] = x h(x)f (x) E[h(X)] = R h(x)f (x)dx
nth moment of X: E[Xn]
nth central moment of X: E[(X − E[X]n]
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.
´ R
arrivals observed between time 0 and time t.
R R
´
