Expectation and variance of a discrete random variable · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

Discrete probability distributions — objective 1

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.

Fresh review variant

Discrete probability distributions — objective 1

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.

Method

Discrete probability distributions — objective 2

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.

Fresh review variant

Discrete probability distributions — objective 2

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.

Apply

Coding and combined data — objective 3

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.

Fresh review variant

Coding and combined data — objective 3

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.

Check understanding

Coding and combined data — objective 4

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.

Fresh review variant

Coding and combined data — objective 4

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.

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