Answer to Question #45517 in Statistics and Probability for sneha jog

Question

(a) A player tosses 3 fair coins. He wins Rs.500 if 3 heads appear, Rs.300 if 2 heads appear, Rs.100 if 1 head occurs. On the other hand, he loses Rs.1500 if 3 tails occur. Find the expected gain of the player and variance.
(b) The trouble shooting capability of an IC chip in a circuit is a random variable X whose distribution function is given by where x denote the number of years. Find the probability that the IC chip will work properly (i) less than 8 years (ii) beyond 8 years (iii) between 5 to 7 years