(2 points) Problem 23. For the roulette experiment (see Lecture 1-3 notes), defi

Question

(2 points) Problem 23. For the roulette experiment (see Lecture 1-3 notes), define the random variable X as X = (1 0 if the marble lands on an odd number otherwise What kind of random variable is x? (Provide the distribution name and all parameter values.) (2 points) Problem 24. Suppose you repeat the roulette experiment four times in a row and define Ys the number of times the marble lands on an odd number. Assuming the four repetitions are independent, what kind of random variable is Y? (Provide the distribution name and all parameter values.) (2 point) Problem 25. In the previous problem, what is the probability that an odd number occurs on at least one of the four repetitions? 7/9

Explanation / Answer

a)
X is bernoulli distribution with p = 18/38

b)
Y = X1 + X2+X3+X4
Y follow binomial distribution with n = 4 , p = 18/38

c)
P(Y >= 0)
= 1 - P(X = 0)
= 1- (1-p)^4
= 1 - (20/38)^4
= 0.9232663960

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