Question

An oil exploration firm is formed with enough capital to finance ten explorations. The probabil- ity of a particular exploration being successful is .1. Assume the explorations are independent. Find the mean and variance of the number of successful explorations.

Answer 1

μ = 1 The firm expects that one oil exploration will be successful.

v(x)= 0.9

Explanation:

The first step is to define the random variable x as:

x: number of oil explorations being succesful

Then x can be take this values:

x = 0 , x =1 ... x =10

x is a binomially distributed random variable with parameters.

p = 0.1 and n=10

And the mean or the expected value of x is:

μ = E(x) = np

Then μ = 10*0.1 = 1

And the variance of x is:

V(x) = np(1-p)

V(x) = 10(0.1)(1-0.1)= 0.9