Question

At a certain coastal location, it is possible to have up to 3 whale sightings per day. The pmf of this distribution is estimated to be as follows.

p(0) = 0.1, p(1) = 0.3, p(2) = 0.4, and p(3) = 0.2.
What are the expected value and standard deviation for this distribution?

Answer 1

Solution :

Mean = = X * P(X)

= 0 * 0.1 + 1 * 0.3+ 2 * 0.4 + 3 * 0.2

= 0 + 0.3 + 0.8 + 0.6

= 1.7

Expected value = 1.7

Standard deviation =

=X ² * P(X) - ²

=  0 * 0.1 + 1 * 0.3+ 2² * 0.4 + 3² * 0.2 - 1.7²

= 0.81

= 0.9

standard deviation for this distribution is 0.9