The random variable X has mean 12 and standard deviation 3. The random variable W is defined as W=7+2X . What are the mean and standard deviation of W ?

The mean and standard devaition of W are 6 and 31 respectively.

Step-by-step explanation:

Given that:

W = 7 + 2X

Variance (W) = Variance(7 + 2X)

For a term constant term, the variance is zero.

So;

W = 4 × Var(X)

W = 4 × (SD (X))²

W = 4 × (3)²

W = 4 × 9

W = 36

Thus, Variance (W) = 36

The standard deviation of W =

W =

W = 6

Also;

E(W) = E(7 +2 X)

E(W) = 7 + 2 × E(X)

where;

mean X = 12

E(W) = 7 + 2(12)

E(W) = 31

Thus, the mean and standard devaition of W are 6 and 31 respectively.