Generating function for a random variable
The moment generating function for a random variable X is given by Mx(t) = (1/4)+ (3/4)*(1/(1-t)), t>1. Determine formulas for the density function and distribution function. Sketch graphs for fx and Fx.
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Prove that the space P of all polynomials is an infinite-dimensional vector space. [Hint: mathematical induction may be useful here.]
Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. Find the probability that a randomly selected adult had an IQ greater than 131.5 (the requirement for membership in the Mensa organiz
Find the probability that a randomly selected adult had an IQ greater than 120.0 (the requirement for membership in the Mensa organization). Round to the nearest thousandth.
What would be the 95th percentile IQ scores? What is the probability that a mean IQ score for a random sample of 40 people will exceed 104.0?
If a population has a standard deviation of 18, what is the minimum number of samples that need to be averaged in order to be 95% confident that the average of the means is within 2 of the true mean?
A previous analysis of paper boxes showed that the the standard deviation of their lengths is 13 millimeters. A packer wishes to find the 95% confidence interval for the average length of a box. How many boxes does he need to measure to be accurat
A study of peach trees found that the average number of peaches per tree was 725. The standard deviation of the population is 105 peaches per tree. A scientist wishes to find the 90% confidence interval for the mean number of peaches per tree.
In a study using 15 samples, and in which the population variance is unknown, the distribution that should be used to calculate confidence intervals is
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