X is the number of times you play the lottery until you win. (We\'ll assume that

Question

X is the number of times you play the lottery until you win. (We'll assume that once you win you stop playing!) X is the number of women in a randomly chosen sample of 500 New York City residents. For the experiment, flip a coin until heads shows, assume that the probability of heads on one flip is 3/4. We define a RV X = the number of flips. What are the possible values of X? Find the probability distribution function for X: give the first four values, and then find a general formula for the probability that X = n Prove that the sum of all the probabilities is 1 using the formula for the sum of a geometric series. Find the probability that X will be no more than 10. You may find U, helpful to use the formula for a partial sun, of a geometric series, or you may use another method (but you must explain or she. ho. you computed your result, as in all of these problems).

Explanation / Answer

1) 1,2,3,4,.....

2)0.75,0.1875,0.046875,0.01171875

P(X=n) = 3/(4)^n

3)sum of probabilities = (3/4) + (1/4)(3/4) + (1/4)^2(3/4) + .... = (3/4) * (1+1/4 + 1/4^2 + ....) = 3/4 * (1/(3/4)) = 1

4) P(X<=10) = (3/4) + (1/4)(3/4) + (1/4)^2(3/4) + ... + (3/4)(1/4)^9 = 1 - (1/4)^10 = 0.9999990463

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