Table of Finding Probabilities: Continuous Distributions


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Problem
Statement
P( X < A ) P( X > A ) P( A < X < B ) P( X < A  or  X > B )
This assumes A<B.
Restatement
using only <  
P( X < A ) 1 - P( X < A ) P( X < B ) – P( X < A ) P( X < A ) + 1 - P( X < B )
Standard
Normal
N( 0, 1 )
pnorm( A ) 1 – pnorm(A)
or
pnorm( A, lower.tail=FALSE )
pnorm( B ) – pnorm( A ) pnorm( A ) + ( 1 – pnorm( B ) )
or
pnorm( A ) + pnorm( B, lower.tail=FALSE)
Non-Standard
Normal
N( C, D )
pnorm( A , mean=C, sd=D) 1 – pnorm(A, mean=C, sd=D)
or
pnorm( A, mean=C, sd=D, lower.tail=FALSE )
pnorm( B, mean=C, sd=D ) – pnorm( A, mean=C, sd=D ) pnorm( A, mean=C, sd=D ) + ( 1 – pnorm( B, mean=C, sd=D ) )
or
pnorm( A, mean=C, sd=D ) + pnorm( B, mean=C, sd=D, lower.tail=FALSE)
Student's t with E degrees of freedom pt( A ,E) 1 – pt(A,E)
or
pt( A,E, lower.tail=FALSE )
pt( B,E ) – pt( A,E ) pt( A,E ) + ( 1 – pt( B,E ) )
or
pt( A,E ) + pt( B,E, lower.tail=FALSE)
χ² with E degrees of freedom pchisq( A ,E) 1 – pchisq(A,E)
or
pchisq( A,E, lower.tail=FALSE )
pchisq( B,E ) – pchisq( A,E ) pchisq( A,E ) + ( 1 – pchisq( B,E ) )
or
pchisq( A,E ) + pt( B,E, lower.tail=FALSE)
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©Roger M. Palay     Saline, MI 48176     October, 2018