# random variable probability question

• Aug 8th 2007, 02:48 PM
earachefl
random variable probability question
Given a random variable x whose probability distribution is:

x = 0, P(x) = .03125
x = 1, P(x) = .15625
x = 2, P(x) = .3125
x = 3, P(x) = .3125
x = 4, P(x) = .15625
x = 5, P(X) = .03125

determine the probability that $(\mu - 2\sigma \leq x \leq \mu + 2\sigma)$.

I get $\mu = 2.5, \sigma \approx 1.118$, so the equation should be $P(.264 \leq x \leq 4.736)$ but I can't remember how to figure the probability from that! I know that the Empirical rule tells us that for a mound shaped distribution, the probability should be approx. .95, but how to figure it exactly?
• Aug 8th 2007, 08:37 PM
TKHunny
For starters, you had better read up on WHEN the Emperical Rule might apply. You may wish to restrict its use to Normal or Near Normal distributions. This little guy with discrete data and only a few possible outcomes may not fit very well. Tchebychev may have similar things to say, but that still may not conclude your examination.

For enders, you're done! You have a good interval. What data points fall within it? Add up their probabilities and call it a day. :)
• Aug 8th 2007, 10:02 PM
CaptainBlack
Quote:

Originally Posted by earachefl
Given a random variable x whose probability distribution is:

x = 0, P(x) = .03125
x = 1, P(x) = .15625
x = 2, P(x) = .3125
x = 3, P(x) = .3125
x = 4, P(x) = .15625
x = 5, P(X) = .03125

determine the probability that $(\mu - 2\sigma \leq x \leq \mu + 2\sigma)$.

I get $\mu = 2.5, \sigma \approx 1.118$, so the equation should be $P(.264 \leq x \leq 4.736)$ but I can't remember how to figure the probability from that! I know that the Empirical rule tells us that for a mound shaped distribution, the probability should be approx. .95, but how to figure it exactly?

$P(.264 \leq x \leq 4.736)=P(x=1) + P(x=2)+P(x=3)+P(x=4)$

or:

$P(.264 \leq x \leq 4.736)=1 - P(x=0) + P(x=5)$

RonL