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The moment generating function for a random variable X is MX(t) = eαt+βt2/2. Find the mean and variance of X.
Statistics and Probability, Statistics
The stock of company TYK pays dividends annually, with next year's dividend expected to be $1 a share. For the next seven years, dividends are expected to grow at a rate of 6% a year. Thereafter, dividends are expected t ...
You have a bag with three fair dice. One is 4-sided, one is 6-sided, and one is 12-sided. You reach into the bag, pick one die at random, and roll it. The outcome of the roll is 4. What is the probability that you rolled ...
The Everly Equipment Company's flange-lipping machine was purchased 5 years ago for $70,000. It had an expected life of 10 years when it was bought and its remaining depreciation is $7,000 per year for each year of its r ...
You want to borrow $36,000 from your local bank to buy a new sailboat. You can afford to make monthly payments of $750, but no more. Assuming monthly compounding, what is the highest rate you can afford on a 60-month APR ...
Consider the probability distribution shown below. x 0 1 2 P(x) 0.65 0.30 0.05 Compute the expected value of the distribution. Compute the standard deviation of the distribution. (Round your answer to four decimal places ...
Suppose a stock has just paid a $4.4 per share dividend (D 0 ). The dividend is projected to grow at 15% for the next three years, then 6% thereafter indefinitely. What should be the amount of dividend in four year ...
The proportion of people who love dogs is known to be 75 % Australia wide. A town in far north Queensland is often different in many aspects to the rest of Australia. When 88 families were sampled the proportion who love ...
Let X(bar) 6 denote the sample mean of a sample X 1 , X 2 , ..., X 6 from Unif (-1, 3). (a) What is the expected value of X(bar) 6 ? (b) What is the variance of X(bar) 6 ?
Michael invested $1,000 in large U.S. stocks at the beginning of 2012. This investment earned 17.90 percent in 2012, 32.00 percent in 2013, 13.50 percent in 2014, and 3.00 percent in 2015. What return did he earn in the ...
The length of timber cuts are normally distributed with a mean of 95 inches and a standard deviation of 0.52 inches. In a random sample of 45 boards, what is the probability that the mean of the sample will be between 94 ...
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