Mean (E(X)) and variance (Var(X)) using 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 \(\displaystyle G_{X}(t)= \frac{10+ 11t+ 13t^{2}}{34}\).

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 \(\displaystyle G_{X}(t)= \frac{11+ 12t+ 14t^{2}}{37}\).

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 \(\displaystyle G_{X}(t)= \frac{11+ 12t+ 14t^{2}}{37}\).

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 \(\displaystyle G_{X}(t)= \frac{12+ 13t+ 15t^{2}}{40}\).

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 \(\displaystyle G_{X}(t)= \frac{12+ 13t+ 15t^{2}}{40}\).

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

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

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

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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