Three performers are invited to an audition. Assume all three performers arrive on their own. Here, the probability of any one of them being late is 0.2. Let X be the number of late participants of the seminar. (a) How do I find the distribution (pmf) of X? (b) How would I calculate the mean and variance of X?
Three performers are invited to an audition. Assume all three performers arrive on their own. Here, the
(a) How do I find the distribution (pmf) of X?
(b) How would I calculate the mean and variance of X?
Identify the random variable: In this problem, the random variable is X, which represents the number of late participants among the three performers.
Determine the probability of success and failure: You are given that the probability of any one performer being late is 0.2, so p (probability of success) is 0.2, and (1 - p) is the probability of not being late, which is 0.8.
Recognize the binomial distribution: Since each performer's lateness is independent, and you want to find the probability distribution of the number of late performers out of a fixed number of trials (in this case, 3 trials), you can use the binomial distribution.
Calculate the probability mass function (pmf): Use the binomial distribution formula to calculate the probabilities of different values of X (the number of late participants) for k = 0, 1, 2, and 3.
- Since the distribution is binomial.
Formulae for mean and variance of X:
E(X) = np ; n -> number of trials ; k = 0,1,...,n ; here n = 3
Var(X) = np(1-p)
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