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Worked solution

Find a mode and a unique median

The discrete random variable XX has distribution

xx01234
P(X=x)P(X=x)0.100.200.300.250.15

Find the mode and median of XX.

CJC · Lecture · Example 6

Choose the largest probability

The mode is 22 because P(X=2)=0.30P(X=2)=0.30 is the largest mass.

How did this part go?

Check both probability halves

P(X≤2)=0.1+0.2+0.3=0.6≥0.5P(X\le2)=0.1+0.2+0.3=0.6\ge0.5 and P(X≥2)=0.3+0.25+0.15=0.7≥0.5P(X\ge2)=0.3+0.25+0.15=0.7\ge0.5. Hence the median is 22. The two inequalities use probability, not the middle position in the list of possible values.

How did this part go?

Common mistakes

A mode maximizes probability; a median divides probability into two halves. They happen to coincide here but need not coincide in general.

Read the hint