The probability density function: check 1
Difficulty: ★★☆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.
The probability density function: review variant 1
Difficulty: ★★☆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.
The probability density function: check 2
Difficulty: ★★☆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.
The probability density function: review variant 2
Difficulty: ★★☆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.
The probability density function: check 3
Difficulty: ★★☆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.
The probability density function: review variant 3
Difficulty: ★★☆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.
The probability density function: check 4
Difficulty: ★★☆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 P(X≤1).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
The probability density function: review variant 4
Difficulty: ★★☆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 P(X≤1).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.