Question

two numbers are selected at random (without replacement) from positive integers 2, 3, 4, 5, 6 and 7. let x denote the larger of the two numbers obtained, find the probability distribution of x.

Answer 1

To find the probability distribution of X, which denotes the larger of two numbers selected without replacement from {2, 3, 4, 5, 6, 7}, one must list all possible pairs, count occurrences of each number as the larger one, and calculate probabilities for each value.

Step-by-step explanation:

Probability Distribution of a Random Variable

When two numbers are selected at random without replacement from the set {2, 3, 4, 5, 6, 7}, and let X denote the larger of the two numbers, the probability distribution of X can be found as follows:

1. List all possible pairs of numbers and identify the larger number in each pair.
2. Count how many times each number occurs as the larger number.
3. Calculate the probability for each number by dividing the count by the total number of pairs.

The larger number can be 3, 4, 5, 6, or 7, and these values are considered for the probability distribution. By considering the set's nature and way of forming pairs, each number will have a different probability of being the larger number.

For example, the probability that X is 7 will stem from the fact only one pair has 7 as its larger number: (6,7). On the other hand, for X to be 3, the only pair is (2,3). Since there are 15 distinct pairs overall, we can calculate specific probabilities for each potential value of X.

To sketch a graph of this discrete probability distribution, you would have points at each possible value of X with their respective probabilities as the heights of these points.