Normally distributed random variables

Not sure about this question, i think the use of letters instead of numbers confuses me. If anyone could provide me with some help, it would be much appreciated

X is a normally distributed random variable. If a<µ<b and Pr(X>a)=p and Pr(X<b)=q, find:

a) Pr(a<X<b)

b) Pr(X<a/X<b)

Re: Normally distributed random variables

Quote:

Originally Posted by

**gbooker** X is a normally distributed random variable. If a<µ<b and Pr(X>a)=p and Pr(X<b)=q, find:

a) Pr(a<X<b)

b) Pr(X<a/X<b)

For part a), $\displaystyle \mathcal{P}(X\le a)=1-\mathcal{P}(X>a)$.

Do you know how to rewrite $\displaystyle \mathcal{P}(a<X<b)~?$

For part b, is that notation suppose to be $\displaystyle \mathcal{P}(X<a|X<B)~?$ OR you you mean $\displaystyle \mathcal{P}(X\color{red}>a|X<B)~?$

Re: Normally distributed random variables

[QUOTE=Plato;679274]For part a), $\displaystyle \mathcal{P}(X\le a)=1-\mathcal{P}(X>a)$.

Do you know how to rewrite $\displaystyle \mathcal{P}(a<X<b)~?$

no I can't think of it, I might have learned it, but I just can't remember it at the moment

For part b, is that notation suppose to be $\displaystyle \mathcal{P}(X<a|X<B)~?$ OR you you mean $\displaystyle \mathcal{P}(X\color{red}>a|X<B)~?$[/QUOTE

sorry about the confusion, i meant the first one

Re: Normally distributed random variables

Quote:

Originally Posted by

**gbooker** Quote:

Originally Posted by

**Plato** For part a), $\displaystyle \mathcal{P}(X\le a)=1-\mathcal{P}(X>a)$.

Do you know how to rewrite $\displaystyle \mathcal{P}(a<X<b)~?$

no I can't think of it, I might have learned it, but I just can't remember it at the moment

For part b, is that notation suppose to be $\displaystyle \mathcal{P}(X<a|X<B)~?$ OR you you mean $\displaystyle \mathcal{P}(X\color{red}>a|X<B)~?$

sorry about the confusion, i meant the first one

In that case note that $\displaystyle (-\infty,a]\cap(-\infty,b]=(-\infty,a]$