probability

[lipsa]

if a random variable X has probability density function given by
F(x)=e^-x   x
     =0        otherwise

find P[2x+3=5]

options
a)1/2
b)1/4
c)0
D)1

[Amit Goyal]

the problem is not written properly. please check and rewrite it.

[lipsa]

sir, i checked its the same... its from gokhle model questions. section c, question 4.
may be the question is wrong!

[Amit Goyal]

The problem is you did not specify under what conditions the density is e^-x. Anyways i am assuming that the density is f(x) = e^{-x} for x>0 and zero otherwise. Then the Pr(2X+3=5)=0.

Explanation: Pr(2X+3=5) = Pr(X=1) = 0 [This is because X is a continuous random variable, therefore Pr(X = c) = 0 for all constant c. You can also integrate the density from 1 to 1 to get the answer]

[Neha Aggarwal]

sir can youb please elaborate how?

[Amit Goyal]

Explanation added to the answer.