The Geometric Distribution (Edexcel A-Level Further Mathematics): Quizzes

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The Geometric Distribution
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What does the geometric distribution describe?

A game with 2 outcomes up to & including 1st win

For X∼Geo(p)X \sim \text{Geo}(p), what does XX represent?

No. of trials up to & including 1st win

Which assumption is required for geometric distribution?

Trials are independent

What probability assumption must hold for X∼Geo(p)X \sim \text{Geo}(p)?

Fixed probability of success

What is P(X=n)P(X = n) for X∼Geo(p)X \sim \text{Geo}(p)?

(1−p)n−1p(1 - p)^{n - 1} p

For X∼Geo(13)X \sim \text{Geo}(\frac{1}{3}), what is P(X=2)P(X = 2)?

29\frac{2}{9}

For X∼Geo(0.7)X \sim \text{Geo}(0.7), what is P(X>5)P(X > 5)?

(0.3)5(0.3)^5

What does P(X≥3)P(X \geq 3) equal for a geometric distribution?

P(X>2)P(X > 2)

How do you calculate P(X≤10)P(X \leq 10) for geometric distribution?

1−P(X>10)1 - P(X > 10)

For X∼Geo(0.7)X \sim \text{Geo}(0.7), how to find P(5≤X<7)P(5 \leq X < 7)?

P(X>4)−P(X>6)P(X > 4) - P(X > 6)

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