Calculating E(g(X)) for a continuous random variable: check 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
X has density \(f(x)=kx^{3}\) for \(0\le x\le 3\) 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.
Calculating E(g(X)) for a continuous random variable: review variant 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
X has density \(f(x)=kx^{1}\) for \(0\le x\le 4\) 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.
Calculating E(g(X)) for a continuous random variable: check 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
X has density \(f(x)=kx^{1}\) for \(0\le x\le 4\) 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.
Calculating E(g(X)) for a continuous random variable: review variant 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
X has density \(f(x)=kx^{2}\) for \(0\le x\le 5\) 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.
Calculating E(g(X)) for a continuous random variable: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
X has density \(\displaystyle \frac{2x}{225}\) on \(0\le x\le 15\). Define \(\displaystyle Y=X^{2}\). For \(0\le y\le 225\), \(\displaystyle F_{Y}(y)= P(X\le \sqrt{y})= \frac{y}{225}\).
Find Var(Y).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Calculating E(g(X)) for a continuous random variable: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
X has density \(\displaystyle \frac{2x}{256}\) on \(0\le x\le 16\). Define \(\displaystyle Y=X^{2}\). For \(0\le y\le 256\), \(\displaystyle F_{Y}(y)= P(X\le \sqrt{y})= \frac{y}{256}\).
Find Var(Y).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Calculating E(g(X)) for a continuous random variable: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
X has density \(\displaystyle \frac{2x}{256}\) on \(0\le x\le 16\). Define \(\displaystyle Y=X^{2}\). For \(0\le y\le 256\), \(\displaystyle F_{Y}(y)= P(X\le \sqrt{y})= \frac{y}{256}\).
Find \(\displaystyle P(Y\le 1)\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Calculating E(g(X)) for a continuous random variable: review variant 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
X has density \(\displaystyle \frac{2x}{289}\) on \(0\le x\le 17\). Define \(\displaystyle Y=X^{2}\). For \(0\le y\le 289\), \(\displaystyle F_{Y}(y)= P(X\le \sqrt{y})= \frac{y}{289}\).
Find \(\displaystyle P(Y\le 1)\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.