Given Y = Log X
and X follows the uniform distribution from 1 to 10, what is Pr(Y > 0.6)?
I have calculated that
X~N(5.5,2.87)
Pr(Y>0.6)
= Pr(Log X> 0.6)
= Pr ( X > 10^(0.6))
= Pr ( X > 3.98)
.
.
.
=0.7
Is my answer correct ?
Actually, when X follows normal distribution, then Y also follows normal distribution right ?
but this time is Y = log x, I am really confused by if Y follows lognormal distribution or not ?
thx :)
Probability Question about Uniform Distribution?
2013-10-13 6:49 am
回答 (2)
2013-10-14 9:50 am
✔ 最佳答案
Forget about the Normal distribution for this one - X is uniform. If X ranges from 1 to 10, then the PDF of X is f(x)=1/(10-1)
= 1/9
If Y = log X, then Y ranges from 0 to 1.
So pr(Y>0.6) translates to the pr(X>3.98) which you have correctly done.
So what is Pr(X>3.98) for the PDF given above ?
I'd expect it to be about 1 - (4-1)/(10-1) =
1 - 1/3 = 0.667
What distribution does Y have? If you're not studying "change of variable" technique, don't worry about it.
2015-04-30 4:10 pm
P(Y > t) = P(ln(X) > t ) = P(X > e^t) = (10 - e^t)/9, and for t = .6 , P(T > .6) = (10 - 1.8221)/9 = .9087
收錄日期: 2021-04-13 22:09:59
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