scresthop123
New member
- Joined
- Feb 16, 2010
- Messages
- 7
1. A random variable Y has a uniform distribution over the interval (a, b). Derive the variance of Y.
2. If alpha >1, integrate by parts to prove that capital gamma(alpha) = (alpha - 1) multiply by capital gamma(alpha - 1).
3. The automatic opening device of a military cargo parachute has been designed to open when the parachute is 200 meters above the ground. Suppose opening altitude actually has a normal distribution with mean value 200m and standard deviation 30m. Equipment damage will occur if the parachute opens at an altitude of less than 100m. What is the probability that there is equipment damage to at least one of five independently dropped parachutes?
4. Suppose the survival time Y in weeks of a randomly selected male mouse exposed to 240 rads of gamma radiation has a gamma distribution with alpha=8 and beta=15.
a. Find the expected survival time in weeks.
b. Find the standard deviation.
c. Determine the probability that a mouse survives between 60 and 120 weeks.
d. Determine the probability that a mouse survives at least 30 weeks.
5. Suppose the respone time Y at a certain on-line computer terminal has an exponential distribution with expected respone time of 5 seconds.
a. Determine the probability that the response time is at most 10 seconds.
b. Determine the probability that the response time is between 5 and 10 seconds.
Sarah
2. If alpha >1, integrate by parts to prove that capital gamma(alpha) = (alpha - 1) multiply by capital gamma(alpha - 1).
3. The automatic opening device of a military cargo parachute has been designed to open when the parachute is 200 meters above the ground. Suppose opening altitude actually has a normal distribution with mean value 200m and standard deviation 30m. Equipment damage will occur if the parachute opens at an altitude of less than 100m. What is the probability that there is equipment damage to at least one of five independently dropped parachutes?
4. Suppose the survival time Y in weeks of a randomly selected male mouse exposed to 240 rads of gamma radiation has a gamma distribution with alpha=8 and beta=15.
a. Find the expected survival time in weeks.
b. Find the standard deviation.
c. Determine the probability that a mouse survives between 60 and 120 weeks.
d. Determine the probability that a mouse survives at least 30 weeks.
5. Suppose the respone time Y at a certain on-line computer terminal has an exponential distribution with expected respone time of 5 seconds.
a. Determine the probability that the response time is at most 10 seconds.
b. Determine the probability that the response time is between 5 and 10 seconds.
Sarah