Originally Posted by JasonT
So I'm just impatient and would like to know where and how I got wrong.
Question: A company produces a single kind of remote control. The lifespan of the remote control follows normal distribution with mean = 3 years and standard deviation = 4.
3 identical remote controls were purchased. Find the probability that the total lifespan of the first two controls exceed the third control by 0.3 years.
Is it just Prob (x1 + x2 > 0.1 + x3)? If so, can I simplify it to Prob (x1+x2-X3> 0.1)
Yes to both, if the 0.3 in the problem statement was a typo and should have been 0.1. All those blue constants should be the same. (If you intentionally converted 0.3 to 0.3/3 since there were 3 random variables, no)
and subsequently, Prob (x>0.1)?
No, assuming independence (which is surely the intent of the problem) you cannot do that. X1+X2-X3 is a normal random variable. You can compute its mean, variance and standard deviation. X1 is normal with mean 3 and standard deviation 4; X1+X2-X3 is normal with mean 3 but a different standard deviation. Thus the probability that X1 > 0.1 and then X2 > 0.1 is different.