Finding the mean and Std Dev from Geometric probabilityThe 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 p ( X = x ) = p ⋅ ( 1 − p ) ( x − 1 ) I (think this is correct) can calculate like so, the first question, P ( X = 5 ) = 0.3 ( 1 − 0.3 ) 5 − 1 This yields the result of 0.07203 where P(X=5) which I think is correct.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?

Question

Finding the mean and Std Dev from Geometric probabilityThe 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  p  (  X  =  x  )  =  p  ⋅  (  1  −  p      )          (      x      −      1      )      I (think this is correct) can calculate like so, the first question,  P  (  X  =  5  )  =  0.3  (  1  −  0.3      )          5      −      1      This yields the result of 0.07203 where P(X=5) which I think is correct.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?

Arjun Wright · Accepted Answer

Step 1You 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 &quot;success&quot; is p, and X is the number of trials until the first success, then   E  (  X  )  =      1    p      and    Var  (  X  )  =            1      −      p              p      2        ..Step 2In 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.

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?

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