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
I (think this is correct) can calculate like so, the first question,
P(X=5) =
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
$\endgroup$ 21 Answer
$\begingroup$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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