Exercise 13 - Dept. of Statistics, Texas A&M University



An instructor has given a short quiz consisting of two parts. For a randomly selected students, let X = the number of points earned on the first part and Y=the number of points earned on the second part. Suppose that the joint pmf of X and Y is given in the accompanying table.

| y|0 |5 |10 |15 |Total |

|x | | | | | |

|0 |0.02 |0.06 |0.02 |0.10 |0.20 |

|5 |0.04 |0.15 |0.20 |0.10 |0.49 |

|10 |0.01 |0.15 |0.14 |0.01 |0.31 |

|Total |0.07 |0.36 |0.36 |0.21 |1 |

Use this information to answer the following 5 questions.

1. Which of the following is the expected number of points earned on the first part?

(a) 5.55 =E(X)=0(0.2)+5(0.49)+10(0.31)

(b) 8.55

(c) 13.55

(d) 18.55

(e) 21.55

2. Which of the following is the probability of maximum number of points earned in two parts, max(x,y) being 5 pts.?

(a) 0.06

(b) 0.10

(c) 0.15

(d) 0.21

(e) 0.25 =P(max(x,y)=5)=p(0,5)+p(5,0)+p(5,5)

3. Which of the following is the probability of total number of points earned in two parts, x+y being 5 pts.?

(a) 0.06

(b) 0.10 =P(x+y=5)=p(0,5)+p(5,0)

(c) 0.15

(d) 0.21

(e) 0.25

4. Given that students did not earn any points on the first part, what is the probability that they will earn 10 points on the second part?

(a) 0.01

(b) 0.02

(c) 0.10 =P(Y=10|X=0)=p(0,10)/P(X=0)=0.02/0.2

(d) 0.12

(e) 0.20

5. Are X and Y independent?

(a) Yes

(b) No because p(0,0)=0.02 (P(X=0)P(Y=0)=0.2(0.07)=0.014

The tensile strength of paper is modeled by a normal distribution with a mean of 35 pounds per square inch and a standard deviation of 2 pounds per square inch. Answer the following 2 questions using this information.

6. What is the probability that the strength of a paper is less than 40 lb/in2?

(a) 0.0062

(b) 0.25

(c) 0.5364

(d) 0.75

(e) 0.9938 = P(X ................
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