Solution_midterm

Solution_midterm - not continuous variable] 4. First, ball...

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Solution for Mid-term exam 1. P(A B)=P(A)+P(B)-P(A∩B)= P(A)+P(B)=0.5 (as no sharing indicates P(A∩B)=0). similarly, P(C∩B)= P(C)+P(B)=0.75 Also food can only be seized by one fish, either A, B, or C, i.e. P(A)+P(B)+P(C)=1. By solving these three equations, we can get P(A)=0.25 P(B)=0.25 P(C)=0.5 Therefore, C is the best . 2. O = "0il" P(I) = 0.4, P(O|I) = 0.4 P(II) = 0.45, P(O|II) = 0.25 P(III) = 0.15, P(O|III) = 0.1 1 . 0 * 15 . 0 25 . 0 * 45 . 0 4 . 0 * 4 . 0 25 . 0 * 45 . 0 + + =0.39 3. X: time to failure for the component. Assume X follows exponential distribution with mean 4, then x e x f 4 1 4 1 ) ( - = x>0 3 month is 1/4 year So the question is to find P(X<=1/4)=1- 16 / 1 - e =0.06 [you may also assume normal, uniform…but Poisson is not suitable, because it is
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Unformatted text preview: not continuous variable] 4. First, ball bound on each nail can be considered as a Bernoulli trial, with success probability (bound to right side) p=0.5; secondly, such Bernoulli trails are IID at every pegs; Third, to reach the bottom, a ball need 7 bounds, slot location is just the number of success jump. From these 3 aspects, we know X~Binomial(7,0.5) 5. (a) 09-1.97318E ) 6 ( * 2 ) 6 | (| =- =- X P (b) ppm X P 4 . 3 )) 5 . 4 ( 1 ( ) 5 . 7 ( ) 6 | (| = -+- =-6. c=0.1 E(X)=1.1 E(Y)= 1.3 V(X)=0.69 V(Y)= 0.81 E(XY)= 1.3 Cov(X,Y)= -0.13 (X,Y)= -0.17 Weak correlation...
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