Question

select the correct histogram for the probability distribution:

x	p(x)
0	0.19
1	0.17
2	0.27
3	0.16
4	0.21

Explanation:

Step1: Match probabilities to bars

For \(x = 0\), \(P(x)=0.19\); for \(x = 1\), \(P(x)=0.17\); for \(x = 2\), \(P(x)=0.27\); for \(x = 3\), \(P(x)=0.16\); for \(x = 4\), \(P(x)=0.21\). We check each histogram to see if the height of the bar at \(x = 0,1,2,3,4\) matches these probabilities.

Step2: Analyze first histogram

In the first histogram, the heights of the bars at \(x = 0,1,2,3,4\) match the probabilities \(0.19, 0.17,0.27,0.16,0.21\) respectively.

Step3: Analyze other histograms

The second histogram has incorrect probabilities for the values of \(x\) (for example, the bar at \(x = 4\) is much higher than \(0.21\)). The third histogram also has incorrect values (the bar at \(x = 2\) is not \(0.27\)). The fourth histogram has incorrect probabilities as well (the bar at \(x = 1\) is not \(0.17\)).

Answer:

The first histogram.