Help with probability question? Any Bernoulli trial can bo formulated by a discr

Question

Help with probability question?

Any Bernoulli trial can bo formulated by a discrete numeric random variable X with the support S_x = {0, 1} and the PMF f_x (x) = pi^2 (1 - pi)^1 - pi, x = 0, 1 where pi = fx(1) is interpreted as the probability of X = 1 and 1 - pi is interpreted as the probability of X = 0 (whatever "1" and "0" means in the trial). If we randomly select a CSUMB student and lot X = 1 for female and X = 0 male, pi is interpreted as the probability of observing a female student (the proportion of female students at CSUMB). By the definition of moan. E(X) = sigma_x = 0^1 x middot f_x (x) = 0 middot (1 - pi) +1 middot pi = pi. The mean (average) of X is equal to pi. Assuming pi = .62, calculate E(X). b. Express the variance V(X) in terms of pi. c. Assuming pi = .62, calculate V(X).

Explanation / Answer

a.E(X)=pi

We are given pi =0.62

hence the value of E(X)=0.62

b.Variance = E(X^2) - E(X)^2 = p-p^2 = p(1-p)

c.Variance of bernoulis distribiution is given by pi(1-pi) = 0.62*(1-0.62) = 0.2356

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