The probability density function · 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

Continuous densities and moments — objective 1

Maths4U Original · Short practice

X has density \(f(x)=kx^{1}\) for \(0\le x\le 6\) 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

Continuous densities and moments — objective 1

Maths4U Original · Short practice

X has density \(f(x)=kx^{2}\) for \(0\le x\le 2\) 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

Continuous densities and moments — objective 2

Maths4U Original · Short practice

X has density \(f(x)=kx^{2}\) for \(0\le x\le 2\) 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

Continuous densities and moments — objective 2

Maths4U Original · Short practice

X has density \(f(x)=kx^{3}\) for \(0\le x\le 3\) 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

Piecewise densities and cumulative functions — objective 3

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 Var(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 3

Maths4U Original · Short practice

The density is \(f(x)=kx\ (0\le x\le 14),\quad f(x)=k(28-x)\ (14<x\le 28)\), and zero elsewhere.

Find Var(X).

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

Check understanding

Piecewise densities and cumulative functions — objective 4

Maths4U Original · Short practice

The density is \(f(x)=kx\ (0\le x\le 14),\quad f(x)=k(28-x)\ (14<x\le 28)\), and zero elsewhere.

Find \(\displaystyle P(X\le 1)\).

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 4

Maths4U Original · Short practice

The density is \(f(x)=kx\ (0\le x\le 15),\quad f(x)=k(30-x)\ (15<x\le 30)\), and zero elsewhere.

Find \(\displaystyle P(X\le 1)\).

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

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