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Find the mean of the following probability distribution. Round your answer to one decimal place.

[tex]\[
\begin{array}{|c|c|}
\hline
x & P(x) \\
\hline
0 & 0.25 \\
\hline
1 & 0.3 \\
\hline
2 & 0.3 \\
\hline
3 & 0.15 \\
\hline
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
To find the mean of the given probability distribution, we follow these steps:

1. Identify the random variable values and their corresponding probabilities:

[tex]\[ \begin{array}{|r|r|} \hline x & P(x) \\ \hline 0 & 0.25 \\ \hline 1 & 0.3 \\ \hline 2 & 0.3 \\ \hline 3 & 0.15 \\ \hline \end{array} \][/tex]

2. Calculate the mean ([tex]\(\mu\)[/tex]) of the probability distribution:

The formula for the mean of a discrete probability distribution is given by:

[tex]\[ \mu = \sum (x_i \cdot P(x_i)) \][/tex]

Where [tex]\( x_i \)[/tex] are the possible values of the random variable [tex]\( x \)[/tex], and [tex]\( P(x_i) \)[/tex] are their corresponding probabilities.

3. Compute the products [tex]\( x_i \cdot P(x_i) \)[/tex] for each [tex]\( x_i \)[/tex] and [tex]\( P(x_i) \)[/tex]:

[tex]\[ 0 \cdot 0.25 = 0 \][/tex]

[tex]\[ 1 \cdot 0.3 = 0.3 \][/tex]

[tex]\[ 2 \cdot 0.3 = 0.6 \][/tex]

[tex]\[ 3 \cdot 0.15 = 0.45 \][/tex]

4. Sum these products to find the mean:

[tex]\[ \mu = 0 + 0.3 + 0.6 + 0.45 = 1.3499999999999999 \][/tex]

5. Round the mean to one decimal place:

[tex]\[ \mu \approx 1.3 \][/tex]

So, the mean of the given probability distribution is approximately 1.3 when rounded to one decimal place.
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