AMS310%20Summer2011%20hw3-ch4[1]

AMS310%20Summer2011%20hw3-ch4[1] - Homework 3 (Chapter 4)...

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Homework 3 (Chapter 4) Due Wednesday, June 15 1. Given the number of heads obtained in three tosses of a fair coin, find the corresponding events and probability for each value of X. (6 points) 2. Are the following functions probability distributions? Why or why not? (6 points) (a) 2 2 ) ( - = x x f for 4 , 3 , 2 , 1 = x (b) 25 ) ( 2 x x f = for 4 , 3 , 2 , 1 , 0 = x f(x)≥0 (a) f(x 1 )=1/2 (b)∑f(x)≠1 ∑f(x)=1 both (a) and (b) are NOT probability distributions. 3. 30% of the trees in a forest are infested with a parasite. Four trees are selected at random. X: number of trees sampled that have the parasite. Let I: infested, N: not infested. Find the probability and cumulative probability for each value of X. (6 points) 4. Given the following distribution, find the mean and the variance. (9 Points) Outcome X HHH 3 HHT 2 HTH 2 HTT 1 THH 2 THT 1 TTH 1 TTT 0 Value of X P(X=x) F(x) 0 (.3) 0 (.7) 4 =.2401 .2401 1 4(.3)(.7) 3 =.4116 .6517 2 6(.3) 2 (.7) 2 =.2646 .9163 3 4(.3) 3 (.7) 1 =.0756 .9919 4 0 4 1 x f(x) xf(x) (x-µ)² (x-µ)²f(x) 1 .4 .4 9 3.6 2 .1 .2 4 .4 6 .3 1.8 4 1.2 8 .2 1.6 16 3.2 Total 1 (µ)=4 33 (σ²)=8.4
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AMS310%20Summer2011%20hw3-ch4[1] - Homework 3 (Chapter 4)...

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