# An experiment results in either successes or failures each trial (denoted S and F ) and...

###### Question:

An experiment results in either successes or failures each trial (denoted S and F ) and the total experiment is three trials. Here are the possible outcomes of the experiment
{SSS, SSF, SF S, F SS, SF F, F SF, F F S, F F F }
Let the random variable X denote whether or not a success occurred in the experiment. Assume each outcome above is equally likely.

a)    Fully deﬁne the probability distribution of X. Is this a probability mass function or a probability density function?
b) Fully deﬁne the cumulative distribution function of X.
c)    What is E(X)?
d)    What is σ2X?
e)    If the random variable Y represents the number of failures in the experiment, are X and Y indepen-dent? Why or why not?(3 pts)

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