Determine whether the random variable is discrete or continuous In each case, st

Question

Determine whether the random variable is discrete or continuous In each case, state the possible values of the random variable. (a) The number of people in a restuarant that has a capacity of 200. (b) The time it takes to fly from City A to City B (a) Is the number of people in a restuarant that has a capacity of 200 discrete or continuous? O A. The random variable ts continuous The possible values are 0sxs 200 O B. The random variable is discrete. The possible values are x 0, 1, 2, ,200 O C. The random variable is continuous The possible values are x 0, 1 2, 200 O D. The random variable is discrete. The possible values are 0 sxs200 (b) Is the time it takes to fly from City A to City B discrete or continuous? O A. The random variable is continuous. The possible values are t -1,2,3 O B. The random variable is discrete. The possible values are t 1 2 3 lllllll Click to select your answer

Explanation / Answer

(a)

The number of people in the restaurant, is a discrete random variable, since it is finite and countable. So, if the random variable X denotes the number of people in the restaurant and it is discrete because the values of X is specified and it takes the value 0, 1, 2, 3, ......, 200, since, the maximum capacity is 200. Hence the answer is B.

(b)

The time taken to fly from City A to City B, is exactly unidentified and we can determine the time interval and therefore, it is a contimuous random variable. If T denotes the random variable of time taken to fly from City A to City B, it is continuous and the values of T should be T>0, if the time intervala are not mentioned. Hence, the answer is C.

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