Maths4U Original · Short practice

Events follow a Poisson process with constant rate \(\displaystyle \frac{13}{4}\) per hour. Let X count events in one hour.

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

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

Maths4U Original · Short practice

Events follow a Poisson process with constant rate \(\displaystyle \frac{7}{2}\) per hour. Let X count events in one hour.

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

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

Maths4U Original · Short practice

Events follow a Poisson process with constant rate \(\displaystyle \frac{7}{2}\) per hour. Let X count events in one hour.

Find \(\displaystyle P(X\ge 4)\).

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

Maths4U Original · Short practice

Events follow a Poisson process with constant rate \(\displaystyle \frac{15}{4}\) per hour. Let X count events in one hour.

Find \(\displaystyle P(X\ge 5)\).

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

Maths4U Original · Short practice

Events follow a Poisson process with constant rate \(\displaystyle \frac{15}{4}\) per hour. Let X count events in one hour.

Find the expected count over three hours.

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

Maths4U Original · Short practice

Events follow a Poisson process with constant rate \(4\) per hour. Let X count events in one hour.

Find the expected count over three hours.

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

Maths4U Original · Short practice

Events follow a Poisson process with constant rate \(4\) per hour. Let X count events in one hour.

Find the probability of exactly one event in two hours.

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

Maths4U Original · Short practice

Events follow a Poisson process with constant rate \(\displaystyle \frac{17}{4}\) per hour. Let X count events in one hour.

Find the probability of exactly one event in two hours.

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

Maths4U Original · Short practice

There are 1000 independent inspections, each with defect probability \(\displaystyle \frac{3}{2000}\). Let X count defects. Use a Poisson approximation where requested.

Find the approximate Poisson mean.

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

Maths4U Original · Short practice

There are 1020 independent inspections, each with defect probability \(\displaystyle \frac{1}{510}\). Let X count defects. Use a Poisson approximation where requested.

Find the approximate Poisson mean.

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

Maths4U Original · Short practice

There are 1020 independent inspections, each with defect probability \(\displaystyle \frac{1}{510}\). Let X count defects. Use a Poisson approximation where requested.

Approximate \(\displaystyle P(X=0)\).

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

Maths4U Original · Short practice

There are 1040 independent inspections, each with defect probability \(\displaystyle \frac{1}{416}\). Let X count defects. Use a Poisson approximation where requested.

Approximate \(\displaystyle P(X=0)\).

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

Maths4U Original · Short practice

There are 1040 independent inspections, each with defect probability \(\displaystyle \frac{1}{416}\). Let X count defects. Use a Poisson approximation where requested.

Approximate \(\displaystyle P(X\ge 2)\).

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

Maths4U Original · Short practice

There are 1060 independent inspections, each with defect probability \(\displaystyle \frac{3}{1060}\). Let X count defects. Use a Poisson approximation where requested.

Approximate \(\displaystyle P(X\ge 3)\).

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

Maths4U Original · Short practice

There are 1060 independent inspections, each with defect probability \(\displaystyle \frac{3}{1060}\). Let X count defects. Use a Poisson approximation where requested.

Find the exact binomial variance.

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

Maths4U Original · Short practice

There are 1080 independent inspections, each with defect probability \(\displaystyle \frac{7}{2160}\). Let X count defects. Use a Poisson approximation where requested.

Find the exact binomial variance.

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

Maths4U Original · Short practice

\(X\sim\operatorname{Po}(63)\). Use N(λ,λ) when an approximation is requested.

Find the approximating variance.

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

Maths4U Original · Short practice

\(X\sim\operatorname{Po}(66)\). Use N(λ,λ) when an approximation is requested.

Find the approximating variance.

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

Maths4U Original · Short practice

\(X\sim\operatorname{Po}(66)\). Use N(λ,λ) when an approximation is requested.

Approximate \(\displaystyle P(X\le 67)\).

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

Maths4U Original · Short practice

\(X\sim\operatorname{Po}(69)\). Use N(λ,λ) when an approximation is requested.

Approximate \(\displaystyle P(X\le 71)\).

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

Maths4U Original · Short practice

\(X\sim\operatorname{Po}(69)\). Use N(λ,λ) when an approximation is requested.

Find the exact Poisson value \(\displaystyle P(X\le 71)\) for comparison.

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

Maths4U Original · Short practice

\(X\sim\operatorname{Po}(72)\). Use N(λ,λ) when an approximation is requested.

Find the exact Poisson value \(\displaystyle P(X\le 75)\) for comparison.

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

Maths4U Original · Short practice

\(X\sim\operatorname{Po}(72)\). Use N(λ,λ) when an approximation is requested.

Find the continuity-corrected upper boundary for this cumulative event.

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

Maths4U Original · Short practice

\(X\sim\operatorname{Po}(75)\). Use N(λ,λ) when an approximation is requested.

Find the continuity-corrected upper boundary for this cumulative event.

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

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.

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.

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.

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.

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.

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.

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.

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.