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Homework Statement
Suppose that tosses of a biased coin in which it comes up heads with probability 1/4 are independant. The coin is tossed 40 times and the number of heads X is counted. The coin is tossed X more times.
A) Determine the expected total number of heads generated by this process.
B) Determine the variance of the total number of heads by this process
Homework Equations
The Attempt at a Solution
I know that [tex] E[X] = \Sigma X_i P(X_i) [/tex]
and I tried to set it up using the binomial distribution (40CX = 40 "choose" X)
[tex](40CX)(1/4)^X (3/4)^{40 - X} + (XCn)(1/4)^n (3/4)^{X - n)[/tex]
I really got no clue on what to do. Any help would be greately appreciated.