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Consider the following statements associated with conditional probability density function (PDF):
1. The conditional PDF is basically a probability, density function (PDF).
2. The conditional PDF is a non-negative function.
3. The area under a conditional PDF is always equal to 1,
4. The conditional density functions reduce to the marginal density functions.
Which of the statements given above are correct?
  • a)
    1,3 and 4
  • b)
    1, 2, and 3
  • c)
    2,3, and 4
  • d)
    1,2, 3 and 4
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Consider the following statements associated with conditional probabil...
• The conditional PDF is basically a PDF Since i.e. the conditional PDF is a non ­negative function.
Hence, statements 1 and 2 are correct.
 th e area under a conditional PDF is always equal to 1. Hence, statement-3 is also correct.
• If the random variables x and y are statistically independent, then 
This means that the conditional density functions reduce to the marginal density functions. Hence, statement-4 is also correct.
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Most Upvoted Answer
Consider the following statements associated with conditional probabil...
Conditional Probability Density Function (PDF)

Statement 1: The conditional PDF is basically a probability density function (PDF).

- This statement is correct.
- A conditional PDF is a probability density function of a random variable given that another random variable has a specific value.

Statement 2: The conditional PDF is a non-negative function.

- This statement is correct.
- The conditional PDF is a probability density function, and probability density functions are always non-negative.

Statement 3: The area under a conditional PDF is always equal to 1.

- This statement is correct.
- The area under a probability density function is always equal to 1, and the conditional PDF is a probability density function.

Statement 4: The conditional density functions reduce to the marginal density functions.

- This statement is correct.
- When the variables are independent, the conditional PDF reduces to the marginal PDF.

Therefore, the correct answer is option D, which includes all the statements as correct.
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Consider the following statements associated with conditional probability density function (PDF):1. The conditional PDF is basically a probability, density function (PDF).2. The conditional PDF is a non-negative function.3. The area under a conditional PDF is always equal to 1,4. The conditional density functions reduce to the marginal density functions.Which of the statements given above are correct?a)1,3 and 4b)1, 2, and 3c)2,3, and 4d)1,2, 3 and 4Correct answer is option 'D'. Can you explain this answer?
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