Linear transformation
Let T be a linear transformation that maps Rn onto Rn. Show that T-1 exists and maps Rn onto Rn. Is T-1 also one-to-one? If so, prove it. If not, prove that instead.
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Find the following percentiles for the standard normal distribution. Interpolate where appropriate. (Round your answers to two decimal places.) (a) 71st
A computer receives input over a slightly faulty connection. For a particular transmission, 80% of the bits sent consists of 0's; the rest are 1's.
In a chemical experiment, a solution is to be kept at 70 degrees Celsius. At a randomly selected time, the actual temperature is a normal random variable with mean 70 degrees Celsius and standard deviation 0.4 degrees Celsius.
The probability that a student passes Math class is 60% and the probablility the student passes English is 80%. The probability that the student passes is 54%
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?
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