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If two random variables x and y are related by y = 2 – 3x, then the SD of y is given by
- a)–3 × SD of x
- b)3 × SD of x
- c)9 × SD of x
- d)2 × SD of x
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If two random variables x and y are related by y = 2 3x, then the SD ...
Calculation of standard deviation of y using relation with x
Explanation:
To find the standard deviation of y using the relation y = 2 3x, we can use the following steps:
1. First, we need to know the formula for the standard deviation of a random variable. The formula is as follows:
SD = sqrt(Σ(x - μ)² / n)
where SD is the standard deviation, x is the value of the random variable, μ is the mean of the random variable, and n is the number of observations.
2. Next, we need to find the mean and standard deviation of x. Let's assume that we have already done this and found that the mean of x is μx and the standard deviation of x is SDx.
3. Now, we can use the relation y = 2 3x to find the mean and standard deviation of y. The mean of y is:
μy = E(y) = E(2 3x) = 2 + 3E(x) = 2 + 3μx
The standard deviation of y is:
SDy = sqrt(Σ(y - μy)² / n) = sqrt(Σ(2 3x - (2 + 3μx))² / n)
Simplifying this expression, we get:
SDy = sqrt(Σ(3x - 3μx)² / n) = sqrt(9Σ(x - μx)² / n) = 3SDx
4. Therefore, the SD of y is 3 times the SD of x, which means that the correct answer is option B.
Conclusion:
The standard deviation of y can be found using the relation y = 2 3x. By knowing the mean and standard deviation of x, we can derive the mean and standard deviation of y using the formulae given above. The SD of y is 3 times the SD of x.
Explanation:
To find the standard deviation of y using the relation y = 2 3x, we can use the following steps:
1. First, we need to know the formula for the standard deviation of a random variable. The formula is as follows:
SD = sqrt(Σ(x - μ)² / n)
where SD is the standard deviation, x is the value of the random variable, μ is the mean of the random variable, and n is the number of observations.
2. Next, we need to find the mean and standard deviation of x. Let's assume that we have already done this and found that the mean of x is μx and the standard deviation of x is SDx.
3. Now, we can use the relation y = 2 3x to find the mean and standard deviation of y. The mean of y is:
μy = E(y) = E(2 3x) = 2 + 3E(x) = 2 + 3μx
The standard deviation of y is:
SDy = sqrt(Σ(y - μy)² / n) = sqrt(Σ(2 3x - (2 + 3μx))² / n)
Simplifying this expression, we get:
SDy = sqrt(Σ(3x - 3μx)² / n) = sqrt(9Σ(x - μx)² / n) = 3SDx
4. Therefore, the SD of y is 3 times the SD of x, which means that the correct answer is option B.
Conclusion:
The standard deviation of y can be found using the relation y = 2 3x. By knowing the mean and standard deviation of x, we can derive the mean and standard deviation of y using the formulae given above. The SD of y is 3 times the SD of x.
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If two random variables x and y are related by y = 2 3x, then the SD of y is given bya)3 SD of xb)3 SD of xc)9 SD of xd)2 SD of xCorrect answer is option 'B'. Can you explain this answer?
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