1
$\begingroup$

On STAT101 your assessment is based on: Final Exam 50% Learn based on-line assessment 30% Assignments 20% Consider three random variables $X$, $Y$ and $Z$ which respectively represent the exam, on-line assessment total and assignment scores (out of 100%) of a randomly chosen student. Assume that $X$, $Y$ and $Z$ are independent (this is clearly not true, but the answers may be a reasonable approximation). Suppose that past experience suggests the following properties of these assessment items (each out of 100%): $E \left ( X \right ) = 61$, $sd(X) = 20$, $E(Y) = 72$, $sd(Y) = 22$ and $E(Z) =65$, $sd(Z) = 24$.

a) Find the distribution parameters, $E(T)$ and $Var(T)$, for the total mark, $T$, where: $T = 0.5X+0.3Y+0.2Z$.

$\endgroup$
0
2
$\begingroup$

Here are some hints that will hopefuly guide you to the answers.

The expectation $E(T)$ can be obtained using the linearity properties of the expected value.

The variance $\mbox{var}(T)$ can be obtained using the expression of the variance of a sum of random variable and using the independence of $X$, $Y$, and $Z$ to determine the value of the covariance terms that appear.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.