A research study use 1000 men under the age of 55. Suppose that 20% of them carr

Question

A research study use 1000 men under the age of 55. Suppose that 20% of them carry a marker on the male chromosome that indicates an increased risk for high blood pressure. For each of the following question, define your random variable, identify the type of its distribution (with correctly identifying the values of parameters), and then write down what probability the question is asking (NO NEED to calculate it, unless you prefer). (a) Suppose men under the age of 55 arrive for testing for the marker independently, what is the probability that the fifth men who the first one carrying the maker? Define the random variable X: Distribution of X: Probability the question is asking: (b) Suppose men under the age of 55 arrive for testing for the marker independently, what is the probability that the fifth men who is the third one carrying the maker? Define the random variable Y: Distribution of Y: Probability the question is asking: (c) If 10 men under the age of 55 are selected independently and tested for the marker, what is the probability that at least 1 has the marker? Define the random variable Z: Distribution of Z: Probability the question is asking:

Explanation / Answer

Q.2 (A) Define the random variable X

Random variable X is the first person carrying the marker

Distribution of X?

Geometric Distribution

Prrobability of Question?

Pr ( X=5 ) = (1-p)4 p = ( 1- 0.2)4 (0.2 ) = 0.08192 [ p = 0.2]

(b)

Define the random variable Y

Random variable Y is the number of person out of 5 carrying the marker

Distribution of Y?

Negative Binomial Distribution

Prrobability of Question?

Pr ( Y=3) = 4C2 (0.8)2 (0.2)2 * 0.2 = 0.03072

(c)

Define the random variable Z

Random variable Z is the number of person having marker out of 10 persons.

Distribution of Y?

Binomial Distribution where n = 10 and p = 0.2

Prrobability of Question?

Pr ( Z>=1)) = 1- P (Z =0) = 1 - 10C0 (0.2)0 (0.8)10 = 1 - 0.1074 = 0.8926

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