68% percent of comic fans visited a movie theater to see Black Panther. Nine movie viewers are selected at random. Let X be a discrete random variable representing the number of the movie viewers.
- FindP(X=4),P(X=5) and P(X=6).
- Write down an expression forF(y) and the cumulative distribution function(CDF) of X, for all y-values from -inf to inf
- Find the Expected value and Variance of X
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As it stands, I think you misunderstand the notation/definitions. In your problem statement you say "nine movie viewers are selected at random", and then define $X = \{\text{no. of movie viewers}\}$. As it stands
$$\mathbf P[X \geq 9] = 1$$
and therefore $$\mathbf{P}[X = 4] = \mathbf{P}[X = 5] = \mathbf{P}[X = 6] = 0.$$
The follow up questions also have simple answers for this problem description.
I think therefore (and I am guessing) that the problem you want to solve is most likely: "68% of visitors to a cinema see Black Pantha. Nine movie viewers are selected at random, and let $X$ denote the number who watched Black Pantha."
In this context, as a hint you will want to look at properties of Binomial random variables.