Solution to The number of cars sold per day at a local car dealership, along with its … - Sikademy
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Peace Awoke

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.

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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


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