Given the probability distributions shown to the right, complete the following parts. Distribution A Distribution B Xi P(X = x;) Xi P(X =x;) a. Compute the expected value for each distribution. b. Compute the standard deviation for each distribution. c. What is the probability that x will be at least 3 in Distribution A and Distribution B? d. Compare the results of distributions A and B. 0.02 0.50 0.08 0.16 0.24 0.24 0.16 0.08 0.02 1 3 0.50 x 01 234

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**Probability Distributions Analysis**

Given the probability distributions shown to the right, complete the following parts:

### a. Compute the expected value for each distribution.
### b. Compute the standard deviation for each distribution.
### c. What is the probability that x will be at least 3 in Distribution A and Distribution B?
### d. Compare the results of distributions A and B.

**Distribution A:**

\[
\begin{array}{|c|c|}
\hline
x_i & P(X = x_i) \\
\hline
0 & 0.02 \\
\hline
1 & 0.08 \\
\hline
2 & 0.16 \\
\hline
3 & 0.24 \\
\hline
4 & 0.50 \\
\hline
\end{array}
\]

**Distribution B:**

\[
\begin{array}{|c|c|}
\hline
x_i & P(X = x_i) \\
\hline
0 & 0.50 \\
\hline
1 & 0.24 \\
\hline
2 & 0.16 \\
\hline
3 & 0.08 \\
\hline
4 & 0.02 \\
\hline
\end{array}
\]
Transcribed Image Text:**Probability Distributions Analysis** Given the probability distributions shown to the right, complete the following parts: ### a. Compute the expected value for each distribution. ### b. Compute the standard deviation for each distribution. ### c. What is the probability that x will be at least 3 in Distribution A and Distribution B? ### d. Compare the results of distributions A and B. **Distribution A:** \[ \begin{array}{|c|c|} \hline x_i & P(X = x_i) \\ \hline 0 & 0.02 \\ \hline 1 & 0.08 \\ \hline 2 & 0.16 \\ \hline 3 & 0.24 \\ \hline 4 & 0.50 \\ \hline \end{array} \] **Distribution B:** \[ \begin{array}{|c|c|} \hline x_i & P(X = x_i) \\ \hline 0 & 0.50 \\ \hline 1 & 0.24 \\ \hline 2 & 0.16 \\ \hline 3 & 0.08 \\ \hline 4 & 0.02 \\ \hline \end{array} \]
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