Solve with accuracy the following tough questions!

1. It was noted that f (x) = (1/3)e-x/3 represents an exponential distribution which in-turn is used to represent the flow of a mobile conversation. Determine the probability that having a conversation will take more than 5 minutes.

2. Determine the probability that X<2 given a random variable of an exponential distribution that has probability function denoted by f(x) =3e-3x for x>0 = 0 otherwise.

3. Compute the probability forP (X>3) given that a random variable has an exponential distribution =1.

4. Determine and show the expression for the mean of an exponential distribution.

5. It was found out that a certain mathematics book had shown that an exponential distribution is bi-variate. Do you support this statement? If so, why?

6. Determine the reason for a value such as 'e' appearing in normal distribution. Explain your answer.

7. Think of a figure that has in its characteristics a normal curve, what is one of the determinants of the shape of this curve.

8. In a random test, a student was asked to determine the value of a standard deviation given that the area of study was a normal standard variate. Explain.

9. Determine the other term that can be used to refer to normal distribution.

10. Given a diagram representing a normal distribution curve, determine the skewness in the distribution of the curve.