STA Quiz 16 Practice PDF

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STA quiz 16 practice...

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Quiz 16 Review Quiz on sections 4.4 and 4.5, Random variables and the mean and variance of random variables. When answering a question, if you have to calculate the answer, then show the work for it. For each problem answer the questions and find the probabilities.

Figure 1

1. Let X be a random variable whose distribution is defined by Figure 1. i. Is X a continuous or discrete random variable? ii. P(X = 0.4) iii. P(X < 0.4)

P(X ≤ 0.4) P(X > 0.4) P(X ≥ 0.6) P(0.4 ≤ X ≤ 0.6) P(0.4 < X < 0.6)

iv. v. vi. vii. viii.

Y

0

1

2

3

P(Y )

0.6

0.25

0.10

0.05

Table 1

2. Let Y be a random variable whose distribution is defined by Table 1. i. Is X a continuous or discrete random variable? ii. P(Y = 4) P(Y = 0.5) iii. iv. v. vi. vii. viii. ix.

P(Y = 2) P(Y < 2) P(Y ≤ 2) P(Y > 2) P(Y ≥ 2) P(Y ≥ 3)

P(2 ≤ Y ≤ 3) P(2 < Y < 3) P(2 < Y ≤ 3) P(2 ≤ Y < 3)

x. xi. xii. xiii.

3. Let A be a random variable with a normal distribution of mean 100 and variance 10. i. Is X a continuous or discrete random variable? ii. P(A = 92) iii. P(A < 92) P(A ≤ 92) iv. P(A > 92) v. P(A ≥ 108) vi. vii. P(92 ≤ A ≤ 108) viii. What’s the highest value of A in the bottom 20%? ix. What’s the lowest value of A in the top 80%? x. What’s the highest value of A in the bottom 30%? xi. What’s the lowest value of A in the top 60%? xii. What values of A are between the 30th and 40th percentile? 4. Let B be a random variable with a normal distribution of mean 50 and variance 5. i. What is the mean and standard deviation of the random variable C, where C = B + B? ii. What is the mean and standard deviation of the random variable C, where C = B − B? iii. If D is N(40,5), what is the mean and standard deviation of the random variable E, where E = B + D? iv. If D is N(40,5), what is the mean and standard deviation of the random variable E, where E

C

1

P(C )

0.301

D

3

P(D)

0.301

Table 2

= B − D?

2

3

4

5

6

7

0.201

0.102

0.099

0.098

0.096

0.103

4

5

6

7

8

9

0.201

0.102

0.099

0.098

0.096

0.103

5. Let C and D be a random variable whose distributions are defined by Table 2. i. What is the mean of C? ii. What is the variance of C? iii. What is the mean of D? iv. What is the variance of D ? v. What is the mean of C + D? vi. What is the variance of C + D if they are independent? vii. What is the variance of C + D if they are not independent? viii. What is the mean of 4C ? ix. What is the variance of 4C?...