A continuous random variable Y has the following probability density function (pdf) cer, 01 ( gt; 0) y ) Determine c as a function of .

A continuous random variable Y has the following probability density function (pdf) cer, 01 (λ > 0) y ) Determine c as a function of λ. Then, for the case λ=2,evaluate c, calculate the maximum value of f(v), and show this value in a sketch of fo). (b) Determine F(y),the cumulative distribution function (edf) of Y. Then, for the case λ = 2, calculate the value of F(0) and show this value in a sketch of F(y). (c) Determine μ EY as a function of λ , and evaluate determine the value of 2 for which u 0. μ for the case (d) Determine m=Median(Y) as a function of λ, and then evaluate this function for λ = 1, 2, 3, 5 and 10, correct to at least one significant digit. Also, calculate , the value of λ for which m= 0, Then sketch m over the range 1 <=λ<=10, and mark in the points at λ 1, 2, 3, 5, 10 and λ0