Question

determine whether the random variable is discrete or continuous. in each case, state the possible values of the random var(a) the number of fish caught during a fishing tournament.(b) the time it takes for a light bulb to burn out.(a) is the number of fish caught during a fishing tournament discrete or continuous?a. the random variable is discrete. the possible values are ( x = 0,1,2,ldots )b. the random variable is discrete. the possible values are ( xgeq0 ).c. the random variable is continuous. the possible values are ( x = 0,1,2,ldots )d. the random variable is continuous. the possible values are ( xgeq0 ).(b) is the time it takes for a light bulb to burn out discrete or continuous?a. the random variable is discrete. the possible values are ( t>0 ).b. the random variable is discrete. the possible values are ( t = 1,2,3,ldots )c. the random variable is continuous. the possible values are ( t = 1,2,3,ldots )d. the random variable is continuous. the possible values are ( t>0 ).

Explanation:

• For part (a):
• A discrete random variable has countable values. The number of fish caught can be counted as \(0,1,2,\cdots\). It cannot take any value between two non - negative integers (e.g., you can't catch \(1.5\) fish).
• For part (b):
• A continuous random variable can take any value within an interval. Time is a continuous quantity. The time \(t\) it takes for a light bulb to burn out can be any positive real number (\(t>0\)). For example, it could be \(1.2\) hours, \(3.456\) hours etc.

Answer:

(a) A. The random variable is discrete. The possible values are \(x = 0,1,2,\cdots\)
(b) D. The random variable is continuous. The possible values are \(t>0\)