Question

The number of cars sold per day at a local car dealership, along with its corresponding probabilities, is shown in the table. Compute for the mean, variance, and standard deviation of the probability distribution of the random variable X. 

Answer 1

Solution:

Assume the given table is:

$$\begin{array}{c:c} x &Pr(X=x) \\ \hdashline 0 & 0.1 \\ \hdashline 1 & 0.1\\ \hdashline 2 & 0.2\\ \hdashline 3 & 0.3\\ \hdashline 4 & 0.2 \\ \hdashline 5 & 0.1 \end{array}$$

Now, mean$=E(X)=\Sigma x.P(x)=0\times0.1+1\times0.1+2\times0.2+3\times0.3+4\times0.2+5\times0.1$

$=0.1+0.4+0.9+0.8+0.5 \\=2.7$

$E(X^2)=\Sigma x^2.P(x)$

$=0^2\times0.1+1^2\times0.1+2^2\times0.2+3^2\times0.3+4^2\times0.2+5^2\times0.1 \\=0.1+0.8+2.7+3.2+2.5 \\=9.3$

Then, $variance=E(X^2)-[E(x)]^2=9.3-2.7^2=2.01$

And standard deviation$=\sqrt{variance}=\sqrt{2.01}=1.417$