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The geometric (p) distribution on {0, 1, 2, .. }. The geometric (p) distribution is often defined as a distribution on {0, 1, 2, .. .. } instead of { 1, 2, 3, . . .}. A random variable W has geometric (p) distribution on (0, 1, 2, . ..) if
P(W = k qkp (k = 0, 1, . . )
a) Show that this is the distribution of the number of failures before the first success in Bernoulli (p) trials.
b) Find P(W > k) (k = 0, 1, . . .)
c) Find E(W).
d) Find Vαr(W).
Given that the battery still works at 20, 000 km, what is the probability it lasts for at least another 40, 000km?
Y2K Inc. has estimated that half of their twenty workers will be injured in the coming year. The expected severity per occurrence is $1,000. What is the expected loss per exposure?
Standard deviation equal to 500 and 50 hours, respectively. Find the probability that a random sample of 15 bulbs will have an average life of less than 475 hours.
A statistical study reported that a drug was effective with a p-value of .042. (a) Is this true? An effective sample may be found about 42 times in 1000 samples.
What is the probability that the plane will complete its next flight safely?
For the sample of men, performance on the simulator task declined by an average of 2.9 points with s = 4.1. Is this a statistically significant change? Use a two-tailed test with = .05.
What is the probability that a person who has submitted one entry will win the following?
For the passengers in the SRS, what is the approximate probability that the mean length of time for them to get through security will be less than 18 minutes?
According to Money, the average home in Ventura County, California, sells for $647,000. Assume that this sample mean was obtained from a random sample of 200.
If during the busiest periods of the day requests for electronic transfers arrive at the rate of 170 per 10-minute period on average.
a sketch a t -v diagram then draw a circle to indicate the region where you are guaranteed to find ideal gas states on
Three dessert packages to choose from. In how many different ways could the couple select an appetizer package, a main course,and a dessert package?
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