Identify the random variable as either discrete or continuous in each of the following. If the random variable is discrete,

Question

Identify the random variable as either discrete or continuous in each of the following. If the random variable is discrete,

Identify the random variable as either discrete or continuous in each of the following. If the random variable is discrete, list its possible values:

(i) An economist is interested in the number of unemployed graduates in the town of population 1 lakh.

(ii) Amount of syrup prescribed by a physician.

(iii) The person on a high protein diet is interesting to gain weight in a week.

(iv) 20 white rats are available for an experiment. Twelve rats are males. A scientist randomly selects 5 rats, the number of female rats selected on a specific day.

(v) A highway-safety group is interested in studying the speed (in km/hr) of a car at a checkpoint.

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

(i) Let X = number of unemployed graduates in a town.

Since the population of the town is 1 lakh, X takes the finite values.

∴ random variable X is discrete.

Range = {0, 1, 2, …, 99999, 100000}.

(ii) Let X = amount of syrup prescribed by a physician.

Then X takes uncountable infinite values.

∴ random variable X is continuous.

(iii) Let X = gain of weight in a week

Then X takes uncountable infinite values

∴ random variable X is continuous.

(iv) Let X = number of female rats selected on a specific day.

Since the total number of rats is 20 which includes 12 males and 8 females, X takes the finite values.

∴ random variable X is discrete. Range = {0, 1, 2, 3, 4, 5}

(v) Let X = speed of .the car in km/hr.

Then X takes uncountable infinite values

∴ random variable X is continuous.