Question

Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is 9. The standard deviation for this distribution is:

(a) 3
(b) 4
(c) 9
(d) 27

Answer 1

In a Poisson distribution, the standard deviation is the square root of the mean. Given a mean of 9, the standard deviation is √9 = 3, which corresponds to option (a).

Step-by-step explanation:

The question involves a Poisson distribution which is a probability distribution that measures the probability of a given number of events happening in a fixed interval of time or space when these events occur with a known constant mean rate and independently of the time since the last event.

In a Poisson distribution, the mean (μ) is equal to the variance (σ²). Therefore, the standard deviation (σ) is the square root of the mean.

Given that the mean (μ) is 9 for the biased coin tossing, we calculate the standard deviation by taking the square root of the mean:

σ = √μ = √9 = 3

The standard deviation for this distribution is 3, which corresponds to option (a).