Continuous Distributions
10-17-2008
, 03:07 AM
ok this problem is really confusing me and i have no idea how to solve it
If Q~UNIF(0,3) find the probability that the roots of the equation g(t)=0 are real, where g(t) = 4t2 + 4Qt + Q + 2
k so we have a uniform dist with a=0 and b=3 which gives us a pdf = 1/3 0<q<3 and zero otherwise, easy enough but how am i supposed to solve that quadratic
do the same now assuming that Q~EXP(1.5)
same deal here i know the pdf = (1/1.5)e^(-q/1.5) q>0
but i don't understand wtf i'm supposed to do with the quadratic
If Q~UNIF(0,3) find the probability that the roots of the equation g(t)=0 are real, where g(t) = 4t2 + 4Qt + Q + 2
k so we have a uniform dist with a=0 and b=3 which gives us a pdf = 1/3 0<q<3 and zero otherwise, easy enough but how am i supposed to solve that quadratic
do the same now assuming that Q~EXP(1.5)
same deal here i know the pdf = (1/1.5)e^(-q/1.5) q>0
but i don't understand wtf i'm supposed to do with the quadratic
10-17-2008
, 06:16 AM
Quote:
ok this problem is really confusing me and i have no idea how to solve it
If Q~UNIF(0,3) find the probability that the roots of the equation g(t)=0 are real, where g(t) = 4t2 + 4Qt + Q + 2
k so we have a uniform dist with a=0 and b=3 which gives us a pdf = 1/3 0<q<3 and zero otherwise, easy enough but how am i supposed to solve that quadratic
do the same now assuming that Q~EXP(1.5)
same deal here i know the pdf = (1/1.5)e^(-q/1.5) q>0
but i don't understand wtf i'm supposed to do with the quadratic
If Q~UNIF(0,3) find the probability that the roots of the equation g(t)=0 are real, where g(t) = 4t2 + 4Qt + Q + 2
k so we have a uniform dist with a=0 and b=3 which gives us a pdf = 1/3 0<q<3 and zero otherwise, easy enough but how am i supposed to solve that quadratic
do the same now assuming that Q~EXP(1.5)
same deal here i know the pdf = (1/1.5)e^(-q/1.5) q>0
but i don't understand wtf i'm supposed to do with the quadratic
iff the discriminant>=0, so the roots of g(t)=0 are real when
(4Q)2 - 4(4)(Q+2) >=0 or Q2-Q-2 >=0
or (Q-2)(Q+1)>=0. Thus, Q<=-1 or Q>=2.
Now just find P({ Q<=-1 or Q>=2 }).
For Q~UNIF(0,3), this is clearly 1/3 and for Q~EXP(1.5), it's
not hard to work out.
10-17-2008
, 11:18 AM