The independent random variables R and S each have normal distributions. The means of R and S are 10 and 12 respectively, and the variances are 9 and 16 respectively. Find the following probabilities, giving your answer correct to 3 significant figures:
a) P(R < S),
b) P(2R > S1 + S2), where S1 and S2 are two independent observations of S.
Solution:
a)
2)