The probability generating function · 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

Probability generating functions — objective 1

Maths4U Original · Short practice

X has PGF \(\displaystyle G_{X}(t)= \frac{13+ 14t+ 16t^{2}}{43}\).

Find \(\displaystyle P(X=2)\).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Probability generating functions — objective 1

Maths4U Original · Short practice

X has PGF \(\displaystyle G_{X}(t)= \frac{14+ 15t+ 17t^{2}}{46}\).

Find \(\displaystyle P(X=2)\).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Method

Probability generating functions — objective 2

Maths4U Original · Short practice

X has PGF \(\displaystyle G_{X}(t)= \frac{14+ 15t+ 17t^{2}}{46}\).

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

Probability generating functions — objective 2

Maths4U Original · Short practice

X has PGF \(\displaystyle G_{X}(t)= \frac{15+ 16t+ 18t^{2}}{49}\).

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

Probability generating functions — objective 3

Maths4U Original · Short practice

X has PGF \(\displaystyle G_{X}(t)= \frac{15+ 16t+ 18t^{2}}{49}\).

Find Var(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

Probability generating functions — objective 3

Maths4U Original · Short practice

X has PGF \(\displaystyle G_{X}(t)= \frac{16+ 17t+ 19t^{2}}{52}\).

Find Var(X).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Check understanding

Probability generating functions — objective 4

Maths4U Original · Short practice

X has PGF \(\displaystyle G_{X}(t)= \frac{16+ 17t+ 19t^{2}}{52}\).

Find E(X(X−1)).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Probability generating functions — objective 4

Maths4U Original · Short practice

X has PGF \(\displaystyle G_{X}(t)= \frac{17+ 18t+ 20t^{2}}{55}\).

Find E(X(X−1)).

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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