Continuous random variable with probability
Let X be a continuous random variable with probability density function f(x) given by:
f(x) =??1/ 6(x^2 + 3x), if ?3 ? x ? 0
k(x?x2), if 0 < x ? 1
0, otherwise.
(a) Find the value of k.
(b) Find the distribution function F(x)
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If the population mean speed on this stretch of the highway has been 68mph with a standard deviation of 5mph, what is the sample size needed to detect an increase in speed on this stretch of the highway of 10mph? Let ? = 0.02 and ? = 0.05.
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