Question

An integer n,1 < n < 144,picked at random.what is the probability that n is the square of an integer?

Answer 1

Answer:

Contrary to the answers given earlier - all of which were absolutely correct, of course - I'd like to address the case where you're sampling random numbers from the continuous Real line, as opposed to the discrete set of integers between 1 and 20.

In this case, the chosen random number (or the Random variable in the parlance of a statistician) assumes a continuous distribution with a uniform probability density function. X ~ Uniform[1,20]

The numbers of interest are 1,4,9 and 16. However, the Reimann sum of the areas of the rectangles corresponding to these numbers limit to zero. Hence, P[ x ∈ [1,20]\{1,4,9,16}] = 1 - P[x ∈ {1,4,9,16}] = 1.

So, there is an almost sure convergence that the random number chosen will not have an integer square root. I hope this helps. :)

Answer 2

Answer:

ur ans is in attachment

hope it wil hlp u

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