Question

f(x) = (kx + 1)/25 , x = 0, 1, 2, 3, 4. 1. Find the...

f(x) = (kx + 1)/25 , x = 0, 1, 2, 3, 4.
1. Find the value of k that makes f a probability mass function. Graph f.
2. What is the expected number of days a rat will spend in the maze?
3. Find and graph the cumulative distribution of the number of days a rat
will spend in the maze. Conditional on the fact that a rat spends at most
3 days in the maze, what is the probability that a rat spends two days in?
4. Suppose that a rat is to receive from this researcher a food that costs 10
dollars for each of the first two days spent in the maze and 5 dollars for
each day after the first two days, what is the expected expenditure of this
researcher?

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Answer #1

golution - 1) Wikiy EPCT) = 1 E (x+1) 25 R=0,1,2,3,4 K(1) +1 + k(3)41 KCO)+1 25 + + + K(Q)+1 25 K(4) +1 25 25 25 JOK+G 25 10kCumulative distribution from is 25 fco) = fco) = 0.04 F(t) = fro)+ fci) - ja to to :0-16 FCQ) : fco+ fi+fca) = 9 95 0.36. f(3d Eapected Expenditure 3) 14 10 x fco)+ (10+10)$60) + (10+10+5) f(a) f C10+10 + 5+5) f(3) + (10 +10+5+5+5) fcu) = 10 (85) + 2

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