Let Y𝑌 be the random variable Y=2+7X𝑌=2+7𝑋 .i) Compute the mean of Y𝑌 , μY𝜇𝑌 .
Question
Let Y
Y = 2 + 7X
i) Compute the mean of Y, .
Solution
To compute the mean of Y, we need to know the mean of X, denoted as μX.
The mean of Y can be computed using the formula for the mean of a linear transformation of a random variable, which is:
μY = a + b * μX
where:
- a is the constant added to X (in this case, 2)
- b is the constant that X is multiplied by (in this case, 7)
- μX is the mean of X
So, if you know the mean of X, you can substitute it into this formula to find the mean of Y.
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