some doubts

[tanudas]

Q. On which of the following interval(s) must the function f (x) = 2+x^2−x^3
have a root?
a) [−1, 0]
b) [0, 1]
c) [1, 2]
d) [2, 3]

Q. If random variable X has probability density function given by
f(x)= e^-x     x
      = 0 Otherwise
Find P [2x + 3 = 5]
a) 1/2
b) 1/4
c) 0
d) 1

[priyesh]

For question 1 it should be option D, and for question 2 it should be C as P(x=1) =0 (in case of continuous distribution) as there is no limit you have provided in the question.

[RS]

Why D for question 1?

[onionknight]

It'd be c. f(1)=2 and f(2)=-2. It's going to be 0 somewhere between the 2.

[Narasimha]

1. Substitute the lower limit and upper limit of intervals in the given function. The interval in which it changes sign(either positive to negative or vice-versa)is the answer.
Answer is c.

2. May be the answer is 0. As the given function is a continuous one,the probability that it is equal to one specific point is 0.

Am not sure about the second one though.