Came across this, &#x03D5;<!-- ϕ --> = probability of event p ( y , &#x03D5;<!--

Brunton39

Brunton39

Answered question

2022-06-09

Came across this,
ϕ = probability of event
p ( y , ϕ ) = ϕ y ( 1 ϕ ) ( 1 y ) = E x p ( log ( ϕ y ( 1 ϕ ) ( 1 y ) ) ) and now, somehow E x p ( log ( ϕ y ( 1 ϕ ) ( 1 y ) ) ) = E x p [ log ( ϕ 1 ϕ ) y + log ( 1 ϕ ) ]. I looked to use the power rule for logs to bring down the y ( 1 y ) in front, the product rule for logs to get an addition to the equation, and the subtraction rule for logs to get the division part of the expression. Upon simplifying, I don't yield the desired expression

My attempt is shown below:
E x p ( log ( ϕ y ( 1 ϕ ) ( 1 y ) ) ) = E x p [ ( 1 y ) log ( ϕ y ( 1 ϕ ) ) ] = E x p [ ( 1 y ) log ( ϕ y ) + log ( 1 ϕ ) ] = E x p [ ( 1 y ) y log ( ϕ ) + log ( 1 ϕ ) ]
So, now I'm not sure if this can arrive at the right answer

Answer & Explanation

Samantha Reid

Samantha Reid

Beginner2022-06-10Added 22 answers

I'll try not to skip any steps -
p ( y , ϕ ) = ϕ y ( 1 ϕ ) ( 1 y ) = exp [ log [ ϕ y ( 1 ϕ ) ( 1 y ) ] ] = exp [ log ( ϕ y ) + log ( ( 1 ϕ ) ( 1 y ) ) ] = exp [ y log ( ϕ ) + ( 1 y ) log ( 1 ϕ ) ] = exp [ y log ( ϕ ) y log ( 1 ϕ ) + log ( 1 ϕ ) ] = exp [ y ( log ( ϕ ) log ( 1 ϕ ) ) + log ( 1 ϕ ) ] = exp [ y log ( ϕ 1 ϕ ) + log ( 1 ϕ ) ]
Jayla Christensen

Jayla Christensen

Beginner2022-06-11Added 5 answers

Good answer, thanks

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school probability

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?