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Experiment: You roll a fair 6-sided die 5 times. Define the random variable x = number of times you rolled an even number.

The probability of exactly X successes in n trials for a Bernoulli process is:

$$ \bigg(\frac{n!}{X!(n - X)!} \bigg) (\pi^{X}) (1 - \pi)^{n-X}$$

What are the possible values for X? 0-5

What is the value of "n" in this experiment? 5

What is the value of "π" in this experiment?

What is the value of (1-π) in this experiment?

π is the percentage of chance that even numbers are rolled.

I was thinking "π " would be .5, because of 2,4,6 being the only options for rolling even numbers. Although, the dice is rolled 5 times so I don't know if that would change.

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This is a straightforward binomial distribution. B(n,pi) with n= number of trials and pi=probability of an event. n=5 and pi=P(even number)=.5 n and pi are parameters of the distribution. they are independent of one another, so n=5 (or more or less) will not affect the value of pi.

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    $\begingroup$ This goes somewhat beyond the "hints and guidance" requested for answers to self-study questions $\endgroup$
    – Glen_b
    Commented May 1, 2015 at 6:40

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