You are here:   Maths & Stats Home / Teaching program / Junior / MATH1015 / Quizzes / Quiz 5

Quiz 5: Integer-valued random variables

Last unanswered question  Question  Next unanswered question

Question 1

In a production process, one fifth of the articles produced are defective. Ten articles from the production line are randomly selested and inspected. Let X be the number of defective articles in this sample. If the distribution of X is B(n,p), what are the values of n and p ?

a)
n = 10, p = 0.1
   b)
n = 10, p = 0.2
c)
n = 10, p = 1
   d)
n = 0.2, p = 10

 

Not correct. Choice (a) is false.
Your answer is correct.
With p being the probability of an article being defective, p = 1 5 = 0.2 and with n being the sample size, n = 10.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.

Question 2

Suppose X ~ B(10,0.2). Find P(X ≥ 3).

a)
0.8791
   b)
0.1209
c)
0.3222
   d)
0.6778
e)
0.6424

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Your answer is correct.
P(X ≥ 3) = 1 - P(X ≤ 2) = 1 - 0.6778 = 0.3222.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.

Question 3

Suppose X ~ B(10,0.2). Find the probability that X is less than 2.

a)
0.6778
   b)
0.3222
c)
0.6242
   d)
0.3758

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Your answer is correct.
P(X < 2) = P(X ≤ 1) = 0.3758.

Question 4

Suppose that X ~ B(10,0.2). What is the probability that X = 2 ?

a)
0.6778
   b)
0.3020
c)
0.2684
   d)
0.3758

 

Not correct. Choice (a) is false.
Your answer is correct.
P(X = 2) = P (X ≤ 2) - P(X ≤ 1) = 0.6778 - 0.3758 = 0.3020.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.

Question 5

Suppose that X ~ B(10,0.2). What are the mean and variance of X respectively ?

a)
1.6, 4
   b)
2, 2.56
c)
2, 1.6
   d)
2, 1.26
e)
1.6, 2

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Your answer is correct.
The mean of X is np = 10×0.2 = 2. The variance of X is np(1-p) = 10×0.2×0.8 = 1.6
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.

Question 6

Suppose X ~ B(10,0.2). What is the probability that X ≤ 2 or X ≥ 8 ?

a)
0.6780
   b)
0.6779
c)
0.678
   d)
0.0002

 

Not correct. Choice (a) is false.
Your answer is correct.
P(X ≤ 2 or X ≥ 8) = P(X ≤ 2)+ P (X ≥ 8) = P(X ≤ 2)+ (1- P (X ≤ 7)) = 0.6778 +1 - 0.9999 = 0.6779.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.

Question 7

Questions 7-9 use the following data.
 
In the following table, the probability of the random variable X taking the values shown are:

| --X---|0----1---2---3----4-----5--- p(X ) 0.1 0.2 0.3 0.3 0.05 0.05
What is the mean of the distribution ?
a)
1.95
   b)
2.25
c)
2.15
   d)
2.10

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Your answer is correct.
The mean is 0 × 0.1 + 1 × 0.2 + 2 × 0.3 + 3 × 0.3 + 4 × 0.05 + 5 × 0.05 = 2.15
Not correct. Choice (d) is false.

Question 8

Questions 7-9 use the following data.
 
In the following table, the probability of the random variable X taking the values shown are
 

| --X---|0----1---2---3----4----5--- p(X ) 0.1 0.2 0.3 0.3 0.05 0.05
What is the variance of the distribution ?
a)
6.15
   b)
1.5275
c)
2.15
   d)
4.6225
e)
4.00

 

Not correct. Choice (a) is false.
Your answer is correct.
∑ iip(X = i) = 2.15, ∑ ii2p(X = i) = 6.15
⇒ V ar(X) = 6.15 - (2.15)2 = 1.5275.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.

Question 9

Questions 7-9 use the following data.
 
In the following table, the probability of the random variable X taking the values shown are
 

| --X---|0----1---2---3----4----5--- p(X ) 0.1 0.2 0.3 0.3 0.05 0.05
What is the standard deviation of the distribution ?
a)
1.46
   b)
4
c)
2.3333
   d)
1.2359

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Your answer is correct.
The standard deviation = √ -------- V ariance = √------ 1.5275 = 1.2359.

Question 10

An experiment consists of throwing a fair coin until the last two outcomes are both heads. Which of the following statements is true ?

a)
The experiment is binomial.
b)
The probability that only two throws are required is 14 .
c)
The probability that only four throws are required is 116 .
d)
The probability that only eight throws are required is 1- 32 .

 

Not correct. Choice (a) is false.
Your answer is correct.
The probability that only two throws are required is the probability of obtaining a head followed by a head, which is 12 ×12 = 14.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
For questions or comments please contact webmaster@maths.usyd.edu.au