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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, μY \mu_Y .

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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.

This problem has been solved

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