https://file.aiquickdraw.com/mathbot/file/17234463325842g5xuzds.jpg

Fill in the P(X=x) values to give a legitimate probability distribution for the discrete random variable X , whose possible values are -3,3,4,5, and 6.

To make the table represent a legitimate probability distribution, the sum of all the probabilities \( P(X = x) \) must equal 1. Let's denote the missing values as \( P(X = 3) \) and \( P(X = 6) \).

Given:
- \( P(X = -3) = 0.29 \)
- \( P(X = 4) = 0.29 \)
- \( P(X = 5) = 0.30 \)

Let the missing values be \( P(X = 3) = p_1 \) and \( P(X = 6) = p_2 \).

The total probability should sum to 1:

\[
0.29 + p_1 + 0.29 + 0.30 + p_2 = 1
\]

Simplifying, we get:

\[
p_1 + p_2 + 0.88 = 1
\]

\[
p_1 + p_2 = 0.12
\]

Now, the values of \( p_1 \) and \( p_2 \) must be non-negative and add up to 0.12. A simple solution could be:

\[
p_1 = 0.06 \quad \text{and} \quad p_2 = 0.06
\]

So, the completed table is:

\[
\begin{array}{|c|c|}
\hline
\text{Value } x \text{ of } X & P(X = x) \\
\hline
-3 & 0.29 \\
3 & 0.06 \\
4 & 0.29 \\
5 & 0.30 \\
6 & 0.06 \\
\hline
\end{array}
\]

Would you like more details on the calculations or have any other questions?

---

Here are some related questions:

1. What is a probability distribution, and how is it different from a cumulative distribution?
2. Can you explain the properties of a valid probability distribution?
3. How do you determine the expected value of a discrete random variable?
4. What is the variance of a discrete random variable, and how is it calculated?
5. Can the probabilities in a distribution be negative? Why or why not?
6. How does one interpret the sum of probabilities in a probability distribution?
7. What are some common examples of discrete random variables?
8. How would you adjust the probabilities if the value of \( P(X = 5) \) was instead 0.25?

**Tip:** When working with probability distributions, always ensure that the sum of all probabilities equals 1. This is a fundamental property that must be satisfied.

Learn how to calculate a probability distribution for a discrete random variable X with specific probabilities assigned to its possible values. Understand the concept of probability distributions and how to ensure the sum of probabilities equals 1. Suitable for high school students studying probability theory and discrete random variables.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation