Example 9.2.4 A random variable X has a distribution with the density function f (x) = (a + 1)x“ %3! = 0 otherwise %3D and a random sample of size 8 produces the data, 0.2, 0.4, 0.8, 0.5, 0.7 0.9 0.8 0.9. Find the maximum likelihood estimate of the unknown parameter a, it being given that In 0.0145152 =-4.2326 (In denotes natural logarithm),

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A: The provided information is as follows:The random variable is .The p.d.f is given as follows:

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Q: 2 If the probability density of a random variable is given by (k + 2)x³ 0 < x < 1 f(x) = 0.…

A: f(x)=(k+2)x3        0&lt;x&lt;10                           o/wproperities∫f(x)dx=1