A man, in search of a wife, tries two approaches: generous and cheapskate. When

Question

A man, in search of a wife, tries two approaches: generous and cheapskate. When the man tries the generous approach, he ends up spending $1000 on his date, who will, eventually, with probability 0.95 break up with him, but with probability 0.05 marry him. when the man tries the cheapskate approach, he spens $50 on his date, who will eventually break up with him. so far in his life, the man only experienced failure, so he cannot tell which approach works better. He therefore decides to choose an approach(generous or cheapskate) at random.

(a) Assuming the man starts searching today, what is his expected cost to find a wife?

(b) Compute the variance on the amount of money the man ends up spending to find a wife.

Explanation / Answer

Methods are Generous Cheapskate

amt spent 1000 50

p for wife 0.95 0.00

amt spent*p 950 0

Expected cost to find a wife = 950+0 = 950

For variance we find x^2*p also

Methods are Generous Cheapskate

amt spent 1000 50

p for wife 0.95 0.00

amt spent*p 950 0

amt spend^2 *p 950000 0

E(X^2) = 950000

Var(x) = 950000-950^2

= 47500

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