A coin is thrown into the air until the cross falls for the first time, or...
A coin is thrown into the air until the cross falls for the
first time, or until three faces fall.
a) What is the probability distribution for the number of runs
until the process ends?
Determine the mean and standard deviation.
What is the probability that the number of releases required is
greater than one?
Homework Answers
From the above information distribution of X is Negative Binomial. Hence it's results are used to solve the problem.
Here k= 3, p= 1/2, q= 1-p= 1/2.
X ~ NB(3,1/2)
Mean= kq/p= (3*0.5)/0.5= 3
Variance= kq/p^2= 6
S.D.=√varaiance= √6
Required Probability = P(X>1)
=1- [P(X=0)+P(X=1)]
=1-(0.125+0.1875)
= 0.6875
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