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A system has a random number of ?aws that we will suppose is Poisson distributed with mean c. Each of these ?aws will, independently, cause the system to fail at a random time having distribution G. When a system failure occurs, suppose that the ?aw causing the failure is immediately located and ?xed.
(a) What is the distribution of the number of failures by time t?
(b) What is the distribution of the number of ?aws that remain in the system at time t?
(c) Are the random variables in parts (a) and (b) dependent or independent?
The weather in London can be summarised as: if it rains one day there's a 70% chance it will rain the following day; if it's sunny one day there's a 40% chance it will be sunny the following day. Assuming that the prior probability it rained yest..
What sample size would be needed to estimate the true proportion of students at your college
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Repeat this process 10 times or you can draw 10 samples simultaneously using StatTools. Make a histogram of the 10 values of sample means. You are constructing the sampling distribution of sample means. What is the center of your histogram?
The yield strength of a metal bolt has a mean of 6,050 pounds with a standard deviation of 100 pounds. Twenty samples of three bolts were tested, resulting in the means shown below.
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R2 000 is invested at 10% per annum compounded half-yearly. After three months, the interest rate changes to 12% per annum compounded monthly. Find the value of the investment after two years.
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