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Wasn't sure what to call this.. .But here goes I am having trouble solving the following questions, here is the first, and how I have gone about it

The daily probability of sighting a landscape bird near the lake is 0.3. What is the probability that the next sighting occurs five days from now?

Using Geometric Probability

Geo prob formula

I (think this is correct) can calculate like so, the first question,

P(X=5) =enter image description here

This yields the result of 0.07203 where P(X=5) which I think is correct.

However my main problem is the question after it which is,

What are the mean and standard deviation of the time until the next landscape bird is seen?

So my question is how can I calculate the mean and standard deviation using the information I have? I am used to calculating it from a graph or table of statistics...

Any help would be appreciated

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Just use the formula for P(X = x) in the formula for mean and std. deviation and simplify. – echoone Sep 13 '13 at 3:45
I don't understand what formula, i have no values other than the ones in the question? – Sim Sep 13 '13 at 4:14
up vote 1 down vote accepted

You are probably expected to use standard formulas for the mean and variance of the geometric distribution, and not to derive these formulas.

If the probability of "success" is $p$, and $X$ is the number of trials until the first success, then $$E(X)=\frac{1}{p} \qquad\text{and}\qquad \text{Var}(X)=\frac{1-p}{p^2}.$$ In our case, $p=0.3$. Recall that you are asked for the standard deviation, so you will have to take the square root of the variance.

Remark: I have not checked the arithmetic, but your setup for the first question is correct.

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Ah thank you, this is very clear, cheers – Sim Sep 13 '13 at 5:33
You are welcome. As I wrote, you are probably expected to use standard formulas for the mean and variance, and not to derive them. Derivation of the formula for the mean is quite straighftorward. Derivation of the formula for variance is more complicated/ – André Nicolas Sep 13 '13 at 5:38

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