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#1
Ok these are a few qus that i know i should be able to do but after not doing any stats for over a year i cant see where im going wrong.

if a p.d.f is p(s)= 10ds^2 (0<s<0.6) and p(s)= 9d(1-s) (0.6<s<1)

im trying to find d, but if i integrate each of the functions using the limits specified and add them the total probability should be 1, i get (0.72+0.72)d=1
so d would be 1/1.44 and this cant be the case because when s=0.6 the p(s) would equal 2.5 which clearly cant be the case. it is probably something really obvious that im doing wrong.

also if a certain disease afflicts 1 in 1000 people , a medical test is 99% accurate (gives correct result 99% of time), what is the probability that you have the disease if the test indicates that you do? is this something to do with a type 2 error- the kind of qu looks familiar but my memory is not good!

any help would really be appreciated xx
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14 years ago
#2
(Original post by devilschild)
Ok these are a few qus that i know i should be able to do but after not doing any stats for over a year i cant see where im going wrong.

if a p.d.f is p(s)= 10ds^2 (0<s<0.6) and p(s)= 9d(1-s) (0.6<s<1)

im trying to find d, but if i integrate each of the functions using the limits specified and add them the total probability should be 1, i get (0.72+0.72)d=1
so d would be 1/1.44 and this cant be the case because when s=0.6 the p(s) would equal 2.5 which clearly cant be the case. it is probably something really obvious that im doing wrong.
You're right, d = 1/1.44. PDFs can take values above 1 - for example, the PDF of the uniform distribution on [0, 0.5].
(Original post by devilschild)
also if a certain disease afflicts 1 in 1000 people , a medical test is 99% accurate (gives correct result 99% of time), what is the probability that you have the disease if the test indicates that you do? is this something to do with a type 2 error- the kind of qu looks familiar but my memory is not good!
P(have disease | test is positive)
= P(have disease AND test is positive) / P(test is positive)
= (1/1000)(99/100) / [(1/1000)(99/100) + (999/1000)(1/100)]
= 11/122
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