Conditital probability of a random variable.

**Sheld** · March 22nd 2011, 11:18 AM

I given that the pdf of a continuous random variable X is

$f(x) = e^{-x}$ for $x > 0$ and $0$ for $x \leq 0$

I have to find $P(X \leq 2 | X > 1)<br />$
Am I correct in thinking that

$P((X \leq 2) \cap (X > 1)) = P(1 < X \leq 2)$ ?

**dwsmith** · March 22nd 2011, 11:39 AM

Originally Posted by Sheld

I given that the pdf of a continuous random variable X is

$f(x) = e^{-x}$ for $x > 0$ and $0$ for $x \leq 0$

I have to find $P(X \leq 2 | X > 1)<br />$
Am I correct in thinking that

$P((X \leq 2) \cap (X > 1)) = P(1 < X \leq 2)$ ?

Yes.

**Sheld** · March 22nd 2011, 01:02 PM

Thanks for answer. I have another quick question, when they say find the distribution of a random variable X, they mean the cumulative distribution function, right?

**dwsmith** · March 22nd 2011, 01:47 PM

Originally Posted by Sheld

Thanks for answer. I have another quick question, when they say find the distribution of a random variable X, they mean the cumulative distribution function, right?

I think so.

**matheagle** · March 22nd 2011, 04:22 PM

Originally Posted by Sheld

Thanks for answer. I have another quick question, when they say find the distribution of a random variable X, they mean the cumulative distribution function, right?

It can mean either the cumulative or the density.
In this case I would say, it's an exponential with mean, beta=1.

Thread: Conditital probability of a random variable.

LinkBack

Thread Tools

Display

Conditital probability of a random variable.

Similar Math Help Forum Discussions

Probability - transformation of random variable

Probability of a random variable

Binomial Random Variable probability

random variable probability

probability(mean of a random variable)

Search Tags