I just need some help on these problems for my test tomorrow. I do not know how to even start this problem.
1. Suppose the random variable X represents the time until an event occurs and that the probability distribution of X is exponential with a mean of 50 years.
a. Find the median value of X (the median of the probability distribution).
b. Graph the probability distribution of X, with axis labels. Show where the mean and the median lie along the horizontal axis.
c. Find P(X ≤ mean) and compare with P(X ≤ median).
d. Find P(X > 1), P(X > 50) and P(X > 100), the probability that the waiting time is more than 1 year, 50 years and 100 years, respectively.
e. Find P(X > 101 years given that X > 100 years). Compare with P(X > 1).