Question

In: Statistics and Probability

There is a fair coin and a biased coin that flips heads with probability 1/4.You randomly...

There is a fair coin and a biased coin that flips heads with probability 1/4.You randomly pick one of the coins and flip it until you get a heads. Let X be the number of flips you need. Compute E[X] and Var[X]

Solutions

Expert Solution

P[ head come up = 1/4 = 0.25

Possible trial

number of trial (X)	outcome	probability (p)
1	H	1/4
2	TH	(3/4)*(1/4)
3	TTH	(3/4)^2*(1/4)
4	TTTH	(3/4)^3*(1/4)
....

The pattern will be same

Now,

(1)

(2)

Subtract 2 from 1

infinite GP with a = 1/4 and r = 3/4

(3)

(4)

Subtract 4 from 3

(5)

again multiply by (3/4)

(6)

Subtract 6 from 5

orchestra answered 1 year ago

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