Question

Comsider the example of the number of languages spoken by Filipino school children. Define x to be the number of languages in which a randomly chosen Filipino child attending school can hold an everyday conversation. Assume the probability function of X, P(x), is as shown in the following table.

X - 1 2 3 4 5 6

P(x) - 0.663, 0.226, 0.066, 0.019, 0.004

a. What is the mean of X?

b. Find the variance of X.

c.Find the standard deviation of X.

Answer 1

Solution:

X - 1 2 3 4 5 6

P(x) - 0.663, 0.226, 0.066, 0.019, 0.004, 0.022

(a)

$Mean=E(X)=\Sigma x.P(x) \\=1\times 0.663+ 2\times0.226+ 3\times0.066+4\times 0.019+ 5\times0.004+6\times0.022 \\=1.541$

(b)

$E(X^2)=x^2.P(x) \\=1^2\times 0.663+ 2^2\times0.226+ 3^2\times0.066+4^2\times 0.019+ 5^2\times0.004+6^2\times0.022 \\=3.357 \\Variance=\sigma^2=E(X^2)-[E(X)]^2 \\=3.357-1.541^2 \\=0.982319$

(c)

Standard deviation$=\sigma=\sqrt{0.982319}=0.99112007345$