Concept explainers
The special case of the gamma distribution in which α is a positive integer n is called an Erlang distribution. If we replace b by 1/λ in Expression (4.8), the Erlang
It can be shown that if the times between successive events are independent, each with an exponential distribution with parameter λ, then the total time X that elapses before all of the next n events occur has pdff (x; λ, n).
a. What is the
b. If customer interarrival time is exponentially distributed with λ = .5, what is the probability that the tenth customer (after the one who has just arrived)will arrive within the next 30 min?
c. The
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Probability and Statistics for Engineering and the Sciences
- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forwardRespiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.arrow_forward
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