STATS 350 Full Yellow Card.pdf

Page 1 Statistics 350 Help Card Summary Measures Sample Mean n x n xxx x in ∑=+???++= 21 Sample Standard Deviation 1 )( 2 ? ? = ∑ n xx s i 1 22 ? ? = ∑ n xnxi Probability Rules ? Complement rule )(1)( APAP C ?= ? Addition rule General: ) and ()()()or ( BAPBPAPBAP ?+= For independent events: )()()()()or ( BPAPBPAPBAP ?+= For mutually exclusive events: )()()or ( BPAPBAP += ? Multiplication rule General: )|()() and ( ABPAPBAP = For independent events: )()() and ( BPAPBAP = For mutually exclusive events: 0) and ( =BAP ? Conditional Probability General: )( ) and ()|( BP BAPBAP = For independent events: )()|( APBAP = For mutually exclusive events: 0)|( =BAP Discrete Random Variables Mean kkii pxpxpxpxXE +???++=== ∑ 2211)( μ Standard Deviation ( )∑∑ ?=?== 222)().(. μμσ iiii pxpxXds Binomial Random Variables knk pp k n kXP ???? ? ? ?? ? ? == )1()( where )!(! ! knk n k n ? =?? ? ? ?? ? ? Mean npXE X == μ)( Standard Deviation )1().(. pnpXds X ?==σ Normal Random Variables ? σ μ? = ? =? xz deviation standard meannobservatioscore ? Percentile: μσ += zx ? If X has the ),( σμN distribution, then the variable σ μ? = XZ has the )1,0(N distribution. Normal Approximation to the Binomial Distribution If X has the B(n, p) distribution and the sample size n is large enough (namely 10≥np and 10)1( ≥? pn ), then X is approximately ( ))1(, pnpnpN ? . Sample Proportions n xp =? Mean ( ) ppE p == ?? μ Standard Deviation n ppp p )1()?(s.d. ? ? ==σ Sampling Distribution of p? If the sample size n is large enough (namely, 10≥np and 10)1( ≥? pn ) then p? is approximately ? ? ? ? ? ? ? ? ? n pppN )1(, . Sample Means Mean ( ) μμ == XXE Standard Deviation n Xds X σσ ==).(. Sampling Distribution of X If X has the ),( σμN distribution, then X is ( ) ?? ? ? ?? ? ? ? n NN XX σμσμ ,, . If X follows any distribution with mean μ and standard deviation σ and n is