Combining independent Poisson counts · Short practice

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Recall

Independent Poisson counts — objective 1

Maths4U Original · Short practice

Independent one-hour counts have \(\displaystyle X\sim\operatorname{Po}(5),\ Y\sim\operatorname{Po}(\frac{7}{2})\). Both arise from constant-rate Poisson processes.

Find the mean of X+Y.

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

Fresh review variant

Independent Poisson counts — objective 1

Maths4U Original · Short practice

Independent one-hour counts have \(\displaystyle X\sim\operatorname{Po}(\frac{16}{3}),\ Y\sim\operatorname{Po}(\frac{15}{4})\). Both arise from constant-rate Poisson processes.

Find the mean of X+Y.

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

Method

Independent Poisson counts — objective 2

Maths4U Original · Short practice

Independent one-hour counts have \(\displaystyle X\sim\operatorname{Po}(\frac{16}{3}),\ Y\sim\operatorname{Po}(\frac{15}{4})\). Both arise from constant-rate Poisson processes.

Find the variance of X−Y.

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

Fresh review variant

Independent Poisson counts — objective 2

Maths4U Original · Short practice

Independent one-hour counts have \(\displaystyle X\sim\operatorname{Po}(\frac{17}{3}),\ Y\sim\operatorname{Po}(4)\). Both arise from constant-rate Poisson processes.

Find the variance of X−Y.

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

Apply

Independent Poisson counts — objective 3

Maths4U Original · Short practice

Independent one-hour counts have \(\displaystyle X\sim\operatorname{Po}(\frac{17}{3}),\ Y\sim\operatorname{Po}(4)\). Both arise from constant-rate Poisson processes.

Find \(\displaystyle P(X+Y=0)\).

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

Fresh review variant

Independent Poisson counts — objective 3

Maths4U Original · Short practice

Independent one-hour counts have \(\displaystyle X\sim\operatorname{Po}(6),\ Y\sim\operatorname{Po}(\frac{17}{4})\). Both arise from constant-rate Poisson processes.

Find \(\displaystyle P(X+Y=0)\).

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

Check understanding

Independent Poisson counts — objective 4

Maths4U Original · Short practice

Independent one-hour counts have \(\displaystyle X\sim\operatorname{Po}(6),\ Y\sim\operatorname{Po}(\frac{17}{4})\). Both arise from constant-rate Poisson processes.

Find the mean combined count over two hours.

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

Fresh review variant

Independent Poisson counts — objective 4

Maths4U Original · Short practice

Independent one-hour counts have \(\displaystyle X\sim\operatorname{Po}(\frac{19}{3}),\ Y\sim\operatorname{Po}(\frac{9}{2})\). Both arise from constant-rate Poisson processes.

Find the mean combined count over two hours.

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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