Answer to Question #59022 in Statistics and Probability for ABJ

Question

5. A college lecturer never finishes his lecture before the end of the hour and always finishes his lecture within 2 min after the hour. Let X= the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is
f(x)={kx 2 0 0≤x≤2otherwise f(x)={kx20≤x≤20otherwise
what is the probability that the lecture continues for at least 90 sec beyond the end of the hour?
6. Let X be a continuous rv with cdf
F(x)=⎧ ⎩ ⎨ ⎪ ⎪ 0x4 [1+ln(4x )]0 x≤05≤y≤10x>4 F(x)={0x≤0x4[1+ln(4x)]5≤y≤100x>4. What is the pdf of X?