End-of-chapter review exercise 8 · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

Piecewise densities and cumulative functions — objective 1

Maths4U Original · Short practice

The density is \(f(x)=kx\ (0\le x\le 11),\quad f(x)=k(22-x)\ (11<x\le 22)\), and zero elsewhere.

Find k.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Piecewise densities and cumulative functions — objective 1

Maths4U Original · Short practice

The density is \(f(x)=kx\ (0\le x\le 12),\quad f(x)=k(24-x)\ (12<x\le 24)\), and zero elsewhere.

Find k.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Method

Piecewise densities and cumulative functions — objective 2

Maths4U Original · Short practice

The density is \(f(x)=kx\ (0\le x\le 12),\quad f(x)=k(24-x)\ (12<x\le 24)\), and zero elsewhere.

Find E(X).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Piecewise densities and cumulative functions — objective 2

Maths4U Original · Short practice

The density is \(f(x)=kx\ (0\le x\le 13),\quad f(x)=k(26-x)\ (13<x\le 26)\), and zero elsewhere.

Find E(X).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Apply

Transformations of continuous variables — objective 3

Maths4U Original · Short practice

X has density \(\displaystyle \frac{2x}{169}\) on \(0\le x\le 13\). Define \(\displaystyle Y=X^{2}\). For \(0\le y\le 169\), \(\displaystyle F_{Y}(y)= P(X\le \sqrt{y})= \frac{y}{169}\).

Find Var(Y).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Transformations of continuous variables — objective 3

Maths4U Original · Short practice

X has density \(\displaystyle \frac{2x}{196}\) on \(0\le x\le 14\). Define \(\displaystyle Y=X^{2}\). For \(0\le y\le 196\), \(\displaystyle F_{Y}(y)= P(X\le \sqrt{y})= \frac{y}{196}\).

Find Var(Y).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Check understanding

Continuous densities and moments — objective 4

Maths4U Original · Short practice

X has density \(f(x)=kx^{1}\) for \(0\le x\le 4\) and zero elsewhere.

Find the median of X.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Continuous densities and moments — objective 4

Maths4U Original · Short practice

X has density \(f(x)=kx^{2}\) for \(0\le x\le 5\) and zero elsewhere.

Find the median of X.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Try written exam-style problems →