A fair coin is tossed until the first tail is tossed Let X b

A fair coin is tossed until the first tail is tossed. Let X be the number of heads in this experiment. Give the probability distribution of X. (values of X and probability until p(X<0.005 of this experiment).

Solution

A fair coin is tossed until the first tail is tossed. Let X be the number of heads in this experiment. Give the probability distribution of X.

X = number of heads

let number of heads = x

P(tail) = p = 1/2

P(head) = 1-p =1/2

P(X = x) = (1-p)^x *p

probaility distirbution function (PDF)

= p(x) = (1-p)^x *p

= p(x) = (1/2)^x*1/2

= p(x) = (1/2)^(x+1)

Cummlative density function (CDF)

= P(x) = sum (i = 0 to x) (1-p)^i *p

= P(x) = sum (i = 0 to x) (1/2)^(i+1)

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value of X

Probaility => (1/2)^(x+1) < 0.005

=> 2^x >100

=> x > 7

so Minimum value of X = 7

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