The Exponential Distribution (University)
Free printable university probability worksheet on the exponential distribution: F(t) = 1 - e^(-lambda t), tail probabilities, and the mean and standard deviation 1/lambda, all computed from the real formulas.
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Probability & Statistics · Math worksheet
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Date
Math
The Exponential Distribution
For X ~ Exponential(lambda): F(t) = 1 - e^(-lambda t), P(X > t) = e^(-lambda t), and mean = sd = 1/lambda. Round probabilities to 4 decimal places.
- 1.Suppose the waiting time for the next earthquake tremor detected by a sensor is exponentially distributed with rate lambda = 0.8. Find P(X < 1 day), rounded to 4 decimal places.
- 2.Suppose the time until the next network packet arrives is exponentially distributed with rate lambda = 1.25. Find P(X > 1 second), rounded to 4 decimal places.
- 3.Suppose the waiting time for the next earthquake tremor detected by a sensor is exponentially distributed with rate lambda = 0.25. Find P(X > 2 days), rounded to 4 decimal places.
- 4.Suppose the time between customer arrivals at a counter is exponentially distributed with rate lambda = 0.2. Find P(1 < X < 3) in minutes, rounded to 4 decimal places.
- 5.Suppose the time between customer arrivals at a counter is exponentially distributed with rate lambda = 1.25. Find P(X > 3 minutes), rounded to 4 decimal places.
- 6.Suppose the waiting time for the next earthquake tremor detected by a sensor is exponentially distributed with rate lambda = 1 per day. State the mean and the standard deviation of the distribution.
- 7.Suppose the waiting time for the next earthquake tremor detected by a sensor is exponentially distributed with rate lambda = 2. Find P(X > 3 days), rounded to 4 decimal places.
- 8.Suppose the time between customer arrivals at a counter is exponentially distributed with rate lambda = 2. Find P(X < 6 minutes), rounded to 4 decimal places.
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