Suppose px 1 p and px 0 1 - p q find the mean variance

Question

Dichotomous Random Variable

Suppose the random variable X takes on only two values, according to the probability distribution given below.

X	0	1
P(x)	0.4	0.6

a. Find the mean, variance, and standard deviation of X.

b. Suppose P(X = 1) = 0.7, and therefore P(X = 0) = 1 - 0.7 = 0.3. Find the mean, variance, and standard deviation of X.

c. Suppose P(X = 1) = 0.8. Find the mean, variance, and standard deviation of X.

d. Suppose P(X = 1) = p and P(X = 0) = 1 - p = q. Find the mean, variance, and standard deviation of X in terms of p and q.

e. For what values of p (and q) is the variance of X greatest?