Expectation and variance of a discrete random variable: check 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
X takes the values \(0,10,20\) with respective probabilities \(10k,11k,13k\).
Find the normalising constant k.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Expectation and variance of a discrete random variable: review variant 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
X takes the values \(0,11,22\) with respective probabilities \(11k,12k,14k\).
Find the normalising constant k.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Expectation and variance of a discrete random variable: check 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
X takes the values \(0,11,22\) with respective probabilities \(11k,12k,14k\).
Find E(X).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Expectation and variance of a discrete random variable: review variant 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
X takes the values \(0,12,24\) with respective probabilities \(12k,13k,15k\).
Find E(X).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Expectation and variance of a discrete random variable: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
The \(\displaystyle n=16\) observations X have mean 13 and population variance 14. Define \(Y=4X+18\). A second disjoint group has 18 Y-values with mean 74.
Find the sum of Y in the first group.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Expectation and variance of a discrete random variable: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
The \(\displaystyle n=17\) observations X have mean 14 and population variance 15. Define \(Y=2X+19\). A second disjoint group has 19 Y-values with mean 51.
Find the sum of Y in the first group.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Expectation and variance of a discrete random variable: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
The \(\displaystyle n=17\) observations X have mean 14 and population variance 15. Define \(Y=2X+19\). A second disjoint group has 19 Y-values with mean 51.
Find the mean of all Y-values in both groups.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Expectation and variance of a discrete random variable: review variant 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
The \(\displaystyle n=18\) observations X have mean 15 and population variance 16. Define \(Y=3X+20\). A second disjoint group has 20 Y-values with mean 69.
Find the mean of all Y-values in both groups.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.