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If X and Y are 2 independent normal variables with mean as 10 and 12 and SD as 3 and 4, then (X + Y) is normal distribution with
- a)mean = 22 and SD = 7
- b)mean = 22 and SD = 25
- c)mean = 22 and SD = 5
- d)mean = 22 and SD = 49
Correct answer is option 'C'. Can you explain this answer?
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If X and Y are 2 independent normal variables with mean as 10 and 12 a...
Solution:
Given that X and Y are 2 independent normal variables with mean as 10 and 12 and SD as 3 and 4.
To find: Distribution of (X + Y)
Approach:
- Use the properties of mean and variance of the sum of two independent random variables to find the mean and standard deviation of (X + Y).
Properties:
- Mean of sum of two independent random variables = Sum of means of two random variables.
- Variance of sum of two independent random variables = Sum of variances of two random variables.
Calculation:
- Mean of X = 10, Mean of Y = 12
- SD of X = 3, SD of Y = 4
- Mean of (X + Y) = Mean of X + Mean of Y = 10 + 12 = 22
- Variance of (X + Y) = Variance of X + Variance of Y = 3^2 + 4^2 = 9 + 16 = 25
- Standard deviation of (X + Y) = Square root of Variance of (X + Y) = √25 = 5
Hence, the correct answer is option C: mean = 22 and SD = 5.
Given that X and Y are 2 independent normal variables with mean as 10 and 12 and SD as 3 and 4.
To find: Distribution of (X + Y)
Approach:
- Use the properties of mean and variance of the sum of two independent random variables to find the mean and standard deviation of (X + Y).
Properties:
- Mean of sum of two independent random variables = Sum of means of two random variables.
- Variance of sum of two independent random variables = Sum of variances of two random variables.
Calculation:
- Mean of X = 10, Mean of Y = 12
- SD of X = 3, SD of Y = 4
- Mean of (X + Y) = Mean of X + Mean of Y = 10 + 12 = 22
- Variance of (X + Y) = Variance of X + Variance of Y = 3^2 + 4^2 = 9 + 16 = 25
- Standard deviation of (X + Y) = Square root of Variance of (X + Y) = √25 = 5
Hence, the correct answer is option C: mean = 22 and SD = 5.
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If X and Y are 2 independent normal variables with mean as 10 and 12 a...
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If X and Y are 2 independent normal variables with mean as 10 and 12 and SD as 3 and 4, then (X + Y) is normal distribution witha)mean = 22 and SD = 7b)mean = 22 and SD = 25c)mean = 22 and SD = 5d)mean = 22 and SD = 49Correct answer is option 'C'. Can you explain this answer?
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If X and Y are 2 independent normal variables with mean as 10 and 12 and SD as 3 and 4, then (X + Y) is normal distribution witha)mean = 22 and SD = 7b)mean = 22 and SD = 25c)mean = 22 and SD = 5d)mean = 22 and SD = 49Correct answer is option 'C'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If X and Y are 2 independent normal variables with mean as 10 and 12 and SD as 3 and 4, then (X + Y) is normal distribution witha)mean = 22 and SD = 7b)mean = 22 and SD = 25c)mean = 22 and SD = 5d)mean = 22 and SD = 49Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If X and Y are 2 independent normal variables with mean as 10 and 12 and SD as 3 and 4, then (X + Y) is normal distribution witha)mean = 22 and SD = 7b)mean = 22 and SD = 25c)mean = 22 and SD = 5d)mean = 22 and SD = 49Correct answer is option 'C'. Can you explain this answer?.
If X and Y are 2 independent normal variables with mean as 10 and 12 and SD as 3 and 4, then (X + Y) is normal distribution witha)mean = 22 and SD = 7b)mean = 22 and SD = 25c)mean = 22 and SD = 5d)mean = 22 and SD = 49Correct answer is option 'C'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If X and Y are 2 independent normal variables with mean as 10 and 12 and SD as 3 and 4, then (X + Y) is normal distribution witha)mean = 22 and SD = 7b)mean = 22 and SD = 25c)mean = 22 and SD = 5d)mean = 22 and SD = 49Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If X and Y are 2 independent normal variables with mean as 10 and 12 and SD as 3 and 4, then (X + Y) is normal distribution witha)mean = 22 and SD = 7b)mean = 22 and SD = 25c)mean = 22 and SD = 5d)mean = 22 and SD = 49Correct answer is option 'C'. Can you explain this answer?.
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