Determine whether the random variable is discrete or continuous, In each case, state the possible values of the random variable. (a) The number of light bulbs that burn out in the next week in a room with 18 bulbs, (b) The time in minutes required to download a file from the Internet. (a) Is the number of light bulbs that burn out in the next week in a room with 18 bulbs discrete or continuous? A. The random variable is discrete. The possible values are \( 0 \leq x \leq 18 \). B. The random variable is continuous. The possible values are \( x=0,1,2, \ldots, 18 \), The random variable is continuous. The possible values are \( 0 \leq x \leq 18 \), C. The random variable is discrete. The possible, values are \( x=0,1,2, \ldots, 18 \). D. Th
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The random variable in question is indeed discrete! It refers to counting the number of light bulbs that burnout in a week, which are whole numbers. So, the possible values are \( 0, 1, 2, \ldots, 18 \) — meaning you could have anywhere from no bulbs burning out to all 18 bulbs failing. Now, as for the time taken to download a file from the Internet, this is a continuous random variable. It can take any value within a range based on speed and file size, so the possible values are any non-negative real numbers (greater than or equal to 0 minutes). You could have time values like 2.5 minutes, 3.75 minutes, or even longer, which makes it a continuous measurement!
