select the correct histogram for the probability distribution:\n|x|p(x)|\n|0|0.19|\n|1|0.17|\n|2|0.27|\n|3|0…

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.