1 of 8 0-day streak

Linear transformations and totals of independent continuous random variables

Question 1 of 8

Calculator allowed

Let X be the length, in centimetres, of a measured object

The given moments of \(X\) are shown below

Define \(Y\) by the rule

Y=3\,X + 3

(a)1 mark

Which formula gives the expected value of \(Y\) from the moments of \(X\)?

E(Y)=(3)E(X)+(3)(3)

E(Y)=(3)E(X)+(3)

E(Y)=(3)^2\operatorname{Var}(X)+(3)

(b)1 mark

Determine the mean of \(Y\)

Expected value of Y

Format: exact fraction

Which formula gives the variance of \(Y\) from the variance of \(X\)?

\operatorname{Var}(Y)=(3)^2\operatorname{Var}(X)

\operatorname{Var}(Y)=(3)^2\operatorname{Var}(X)+(3)

\operatorname{Var}(Y)=(3)E(X)+(3)

(d)1 mark

Determine the variance of \(Y\)

Variance of Y Format: whole number