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Consider the subsets of a set with n elements that have a cardinality of n and...

Consider the subsets of a set with n elements that have a cardinality of n and n−1. Suppose one of these subsets is chosen at random. What is the expected value of the cardinality of this subset?

Math   Statistics-And-Probability   
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Answer #1

The set has n elements.

Total number of subset of that set, which has cardinality n is 1. Since n element can be chosen in 1 ways.

Total number of subset of that set, which has cardinality n-1 is . Since n - 1 element can be chosen in ways.

hence total number of subset is with cardinality n and n-1 is n+1.

hence the probability of choosing set of cardinality n is

and probability of choosing set of cardinality n - 1 is  

Suppose x is the cardinalty of the set.

So Expectation is

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