Linear combinations and independent normal comparisons: check 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
Independent variables have \(X\sim N(17,3),\ Y\sim N(21,3)\). Put \(Z=2X-Y\). The normal notation uses variance as its second parameter.
Find E(Z).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Linear combinations and independent normal comparisons: review variant 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
Independent variables have \(X\sim N(18,4),\ Y\sim N(23,4)\). Put \(Z=3X-Y\). The normal notation uses variance as its second parameter.
Find E(Z).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Linear combinations and independent normal comparisons: check 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
Independent variables have \(X\sim N(18,4),\ Y\sim N(23,4)\). Put \(Z=3X-Y\). The normal notation uses variance as its second parameter.
Find Var(Z).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Linear combinations and independent normal comparisons: review variant 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
Independent variables have \(X\sim N(19,5),\ Y\sim N(25,5)\). Put \(Z=4X-Y\). The normal notation uses variance as its second parameter.
Find Var(Z).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Linear combinations and independent normal comparisons: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Independent variables have \(X\sim N(19,5),\ Y\sim N(25,5)\). Put \(Z=4X-Y\). The normal notation uses variance as its second parameter.
Find P(Z>54).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Linear combinations and independent normal comparisons: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Independent variables have \(X\sim N(20,2),\ Y\sim N(27,3)\). Put \(Z=2X-Y\). The normal notation uses variance as its second parameter.
Find P(Z>14).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Linear combinations and independent normal comparisons: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
Independent variables have \(X\sim N(20,2),\ Y\sim N(27,3)\). Put \(Z=2X-Y\). The normal notation uses variance as its second parameter.
Find the variance of the sum of three independent copies of X.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Linear combinations and independent normal comparisons: review variant 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
Independent variables have \(X\sim N(21,3),\ Y\sim N(29,4)\). Put \(Z=3X-Y\). The normal notation uses variance as its second parameter.
Find the variance of the sum of three independent copies of X.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.