posterior probability question

**Logical** · Dec 24th 2008, 10:30 PM

hi

in the attachment is the question
I have problem solving it

from question I just knew the Prior Probability for that their claim correct is =0.2 and not correct =0.8
after he did the experiment he found that it is correct 100 %
but I could not find where is the posterior

Prior Probability =0.2
correcting information= 1
posterior =?
until now this is what I came up with

thank you in advance

**mr fantastic** · Dec 25th 2008, 03:27 AM

Originally Posted by Logical

hi

in the attachment is the question
I have problem solving it

from question I just knew the Prior Probability for that their claim correct is =0.2 and not correct =0.8
after he did the experiment he found that it is correct 100 %
but I could not find where is the posterior

Prior Probability =0.2
correcting information= 1
posterior =?
until now this is what I came up with

thank you in advance

Prior: Pr(T > 10) = 0.2

Pr(Data | T > 10) = 1, Pr(Data | T < 10) = 0.

$\Pr(T > 10 \, | \, \text{Data}) = \frac{\Pr(T > 10 \cap \text{Data})}{\Pr(\text{Data})}$ .

$\Pr(T > 10 \cap \text{Data}) = \Pr(\text{Data} \, | \, T > 10) \cdot \Pr(T > 10) = (1) (0.2) = 0.2$ .

$\Pr(\text{Data}) = \Pr(\text{Data} \, | \, T > 10) \cdot \Pr(T > 10) + \Pr(\text{Data} \, | \, T < 10) \cdot \Pr(T < 10)$ $= (1)(0.2) + (0)(0.8) = 0.2$ .

Therefore $\Pr(T > 10 \, | \, \text{Data}) = \frac{0.2}{0.2} = 1$ .

**Logical** · Dec 25th 2008, 03:53 AM

Thank you for helping me

Thread: posterior probability question

LinkBack

Thread Tools

Display

posterior probability question

Similar Math Help Forum Discussions

Is there a difference between posterior denisty and posterior distribution?

Posterior p.f.

Prior and Posterior Distribution Question

posterior

posterior probability

Search Tags