Question

we have n men working on the site. then find a and b

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Answer 1

Let us define a random variable X such that it is a random variable defining number of men working on a day on a site. Then X can be said to follow discrete uniform distribution with parameter n. Now two cases will occur:

Case 1: When minimum one man will be present on the site then p.m.f is drfined as

P(X=x)=1/n ; x=1,2,...,n

On comparing it with standard uniform mass function,

P(X=x)= 1/(b-a) ;

This implies that a=0 and b=n.

Case 2: When the case of no man on the site is also involved.Then p.m.f ofX is defined as:

P(X=x) =1/(n+1) ; x=0,1,2,3,....,n

On comparing it with standard uniform mass function,

P(X=x)=1/(b-a);

Tbis implies that a =0 , b=n+1.

Hence the solution.

Thank you.