The time in minutes, it takes to reboot a certain system

[TomJerry]

Question:
The time in minutes , it takes to reboot a certain system is continuous random variable with density.

f(x) = C(10-x^2), 0<= x <=10 ;
= 0 , other wise
i) compute C
ii)Obtain the probability that it takes between 1 and 2 minutes to reboot.


Solution :

i)
f(x) = $$\int_{0}^{10}$$ C(10-x^2) dx =
.
.
C = - 3 /700 [Is this correct]

ii)
$$\int_{0}^{10}$$ f(x) -[$$\int_{0}^{1}$$ f(x) + $$\int_{2}^{10}$$ f(x)]

[Is this correct]

 

[CompuChip]

I agree with your answer to i), although technically the given function is not a probability density function. In that case, namely, it should be non-negative everywhere, which $-\frac{3}{700} (10 - x^2)$ is not. Are you sure that the 10 is not supposed to be a 100?

For ii), your expression is correct, but it is a bit cumbersome.
Can you prove that what you wrote is actually the same as
$$\int_1^2 f(x) \, dx$$ ?