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 temperature, in degrees Celsius, recorded during a test

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

Define \(Y\) by the rule

Y=3\,X + 4

(a)1 mark

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

E(Y)=(3)E(X)+(3)(4)

E(Y)=(3)^2\operatorname{Var}(X)+(4)

E(Y)=(3)E(X)+(4)

(b)1 mark

Find the expected value 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)E(X)+(4)

\operatorname{Var}(Y)=(3)^2\operatorname{Var}(X)+(4)

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

(d)1 mark

Find the variance of \(Y\)

Variance of Y

Format: exact fraction