Compare this with the given moment generating function and you see that X must follow a normal distribution with and variance .
This gives you a way of checking the answers to 2. and 3.
It also lets you calculate Pr(a < X < b) were it to be asked.
i'm so sorry i solve it before i open my mail and see the solution >>>
i forgot that the derivative for 2te^(t^2 ) is equal to "derivative for two multiply function " so the answer is false >>>>>
but i solve it >>>>>then i verify from your saying
thank you>>>>you're a nice man