End-of-chapter review exercise 8: check 1
Difficulty: ★★☆Info
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.
End-of-chapter review exercise 8: review variant 1
Difficulty: ★★☆Info
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.
End-of-chapter review exercise 8: check 2
Difficulty: ★★☆Info
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.
End-of-chapter review exercise 8: review variant 2
Difficulty: ★★☆Info
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.
End-of-chapter review exercise 8: check 3
Difficulty: ★★☆Info
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.
End-of-chapter review exercise 8: review variant 3
Difficulty: ★★☆Info
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.
End-of-chapter review exercise 8: check 4
Difficulty: ★★☆Info
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.
End-of-chapter review exercise 8: review variant 4
Difficulty: ★★☆Info
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.