Question

Two numbers are select at random (without replacement) from the first five positive integers. Let x denote the larger of the two numbers obtained. Find the mean and variance of x.

Answer 1

This information represents a binomial distribution.

Where:

The number of trials n =2

The probability of getting a larger number P = 1/5

The probability of getting a smaller number q = (1 - p) = 1 - 1/5 = 4/5

Mean of a binomial distribution :

m = np = 1/5 × 2 = 2/5 = 0.4

Variance of a binomial distribution is :

Var = npq = 2 × 1/5 × 4/5 = 8/25 =0.32

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