Business Question

You are required to complete this Statistics assignment professionally and accurately. Please follow all instructions carefully and ensure that the final work is well-organized, clear, and free of errors.

### Task 1:

Write a clear explanation of what a random variable is, and distinguish between discrete and continuous random variables. Your answer must be at least 100 words and written in your own words. Include simple examples to support your explanation.

Then, provide a practical example from a workplace (or daily life if no workplace is available) and identify whether the probability distribution used is discrete or continuous. Explain why, and describe how statistical concepts are applied in that context.

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### Task 2:

Given the probability distribution:

X: 0, 1, 2, 3

P(X=x): k, 0.2, 2k, 0.3, k

You must:

1. Find the value of k using the rule that total probability equals 1.

2. Compute the mean (expected value) of X.

3. Compute the variance of X.

4. Calculate the following probabilities:

– P(X < 1)

– P(X > 0)

– P(X 0)

Show all steps clearly and use correct formulas.

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### Task 3:

Using the given table of 1000 professionals:

– Calculate:

1. P(Favor)

2. P(Oppose)

– Then calculate:

3. P(A1 | G1)

4. P(A1 | G2)

You must:

– Write the probability formulas correctly.

– Show all calculations step by step.

– Provide a brief interpretation of each conditional probability result.

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### Formatting Requirements:

– Use Times New Roman, font size 12, single spacing.

– Include a proper cover page.

– Follow APA referencing style for any sources used.

– Ensure the work is original and plagiarism is below 20%.

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### Important Notes:

– All answers must be accurate and complete.

– Calculations must be clearly shown.

– Explanations should be simple and precise.

– The final document should be ready for direct submission.

Make sure the work meets academic standards and is suitable for full marks.

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