Question

Q2 choose the correct answer:

Suppose that the incidence of a certain subtype of oral cancer is 3.1%among men, and 1.8% among women. However, the percentage ofthe cancer among smoking men is 16%, and is the same as amongsmoking women. In relation to these statistics, which of the followingwould be a correct statement?

(a) The oral cancer subtype and gender are independent, but not in-dependent when conditioned on smoking status.

(b) The oral cancer subtype and gender are not independent, but in-dependent when conditioned on smoking status.

(c) The oral cancer subtype and gender are independent, and alsoindependent when conditioned on smoking status.

(d) The oral cancer subtype and gender are not independent, andalso not independent when conditioned on smoking status.

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b) If electricity power failures in a remote villageV1occur accordingto a Poisson distribution with an average of3 failures every twentyweeks, and the failures in a neighboring villageV2also occur accord-ing to a Poisson distribution with an average of1 failure per fiveweeks. IfXdenotes the total number of power failures in villageV1andV2in twenty weeks, what isE[X]?

(a) 10

(b) 20

(c) 7

(d) 14

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c) Suppose X is a random variable such that E[X] = 5 and V ar (X) = 7, and we define a new random variableY= 3X+ 2. Which of thefollowing is true regardingY?

(a)E[Y] = 15andV ar(Y) = 21

(b)E[Y] = 15andV ar(Y) = 63

(c)E[Y] = 17andV ar(Y) = 21

(d)E[Y] = 17andV ar(Y) = 23

Answer 1

2a)

As we have a different value of % for man and woman so the oral cancel subtype and gender are dependent

but we condition on smoking then both % are the same so it becomes independent when conditioning on smoking

so option b is correct

b)