CEGE 3102-You are the engineer of record for a stream

Problem 2You are the engineer of record (i.e. responsible) for a stream restoration pilot project here in Minnesota. There are four (4) streams of interest. Last Fall you built experimental anti- erosion systems on each of the streams. You hope that the streams will flood this Spring, and overtop their banks, so that you can see how the engineered systems respond.From experience, and the historical record, your boss estimates that the odds of each stream overtopping its banks this Spring (i.e. flooding) is 3 to 1 (i.e. 75 percent chance) for each of the streams. Since the streams are geographically separate – spread out around the state with non-overlapping watersheds – we will model the probability of any one stream flooding as statistically independent5 from that for any of the other streams.If a stream flooding is called a success (designated by an “S”), and everything else is a failure (designated by an “F”), one possible outcome of this “random experiment” is the sequence (SSFS). Let the discrete random variable X be the number of successes; thus, for the outcome (SSFS), X = 3. The discrete random variable X can take on five possible values: {0,1,2,3,4}.Exhaustively enumerate all possible outcomes (i.e. every possible sequence of “S” and “F”). In this case, order matters. There are two possibilities for each stream (S or F), and there are four streams, so there are 24 = 16 possible outcomes.What is the probability of each outcome? Remember that Pr(S) ?= Pr(F).Enumerate the associated values of X. Remember, X is the number of successes.Give the probability mass function for X. You may do this with a table or with a simple graphGive the cumulative distribution function X. You may do this with a table or with a simple graphWhat is the expected value of X?What is the variance of X?what is the standard deviation of X?What is the mode of X?What is the median of X?