Answer to Question #174219 in Statistics and Probability for Aditi Gupta

Question

The time taken X by a garage to repair a car is a continuous rv with pdf f(x) = { 3x 4 (2 − x); 0 ≤ x ≤ 2 0; elsewhere If, on leaving his car, a motorist goes to keep on an engagement lasting for a time Y, where Y is a continuous rv independent of X, with pdf f(y) = { 1 2 y; 0 ≤ y ≤ 2 0; elsewhere . Determine the probability that the car will not be ready on his return. 

Answer 1

$F(x)=3x^4(2-x)$ , $0\le x \le 2$

$f(y)=\dfrac{y}{2}$ , $0\le y\le 2$

Probability that the car will not ready for return $= F(0)\times f(2)+ F(1)\times f(1)+F(2)\times f(0)$

$=3(0)(2-0) \times f(2)+3(1)(2-1)\times 12+\dfrac{2}{2}^4(2-2)\times f(0)$

$=0+1+0=1$