sta301 midterm mcq file 2021

 

STA301 – Midterm Fall 2021

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Question ( Marks: 5 )

The numbers of airplane accidents in a year are 1, 2, 3, 4 with corresponding probabilities 1/6, 2/6, 2/6 and 1/6. What is the variance of annual accidents?

Solution:-

 

X	P	PX	X2	PX2
1	1/6	1/6	1	1/6
2	2/6	2/3	4	4/3
3	2/6	1	9	3
4	1/6	2/3	16	8/3
Total		5/2		43/6

 

 

VAR(X) = E(X)² - EX²

 

 

 

 

 

 

 

 

 

 

Question ( Marks: 3 )

A ball is selected at random from a bag contains 2 white, 5 black and 7 green balls. What is the probability that it is a

1.      White ball

2.      Green ball

 

Solution:-

White Ball =

Black ball =

 

 

Question ( Marks: 3 )

For the given data calculate the mean deviation.

+ 3

- 3

- 4

- 1

+1

+ 4

  Solution:

X
3	3
-3	3
-4	4
-1	1
1	1
4	4

 

Mean = 0

 

 

 

 

 

 

 

Question ( Marks: 2 )

 “If P (A|B) = P (B|A) then P (A) = P (B)”.

Indicate whether the above statement is true or false? Also give reason.

Solution:-

Yes this statement is true, because

Therefore there is difference just in denominator

If the Values of P (A|B) = P (B|A re same then the denominator should also be same

 

Question ( Marks: 2 )

Why we use coefficient of variation?

Answer:- (Page 93)

We calculate variation if we have to compare different data with the same variable but with very different arithmetic means.

 

 

 

 

STA301 – Midterm Fall 2012 (December)

 

Q1: find the missing value in the formula?   ( Marks: 2 )

Answer:- (Page 159)

 P (B) is missing.

 

 

Q2: what is Coefficient of Correlation? ( Marks: 2 )

 Answer:- (Page 128)

A numerical measure of the strength of the linear relationship between two random variables X and Y is
known as Pearson’s Product-Moment Coefficient of Correlation.

 

 

Q3: why the mean of the probability distribution of a random variable X is technically called the EXPECTED VALUE of the random variable X ?     ( Marks: 3 )

 Answer:- (Page 170)

Because we expect the mean from of the random variable from the data.

 

 

 

 

 

Q4: For the give data

Means = 3.8,

Median = 2.3 and

Standard Deviation = 1.3,

Now Find the Pearson's Coefficient of skweness ?   ( Marks: 2 )

Answer:-  

It is positively skewed

 

 

Q5: Compute the mean deviation from mean for the following data (where Mean =  = 40.4)

( Marks: 5 )

 

X	30	35	40	45	50
F	4	7	11	8	5

 

 

 

 

 

Answer:-

X	F	,
30	4	10.4	41.6
35	7	33.4	233.8
40	11	0.4	4.4
45	8	4.6	36.8
50	5	9.6	48

 

 M.D =

 

 

Q: A husband and wife appear in an interview for two vacancies in the same post. The probability of husband’s selection is 2/7 and probability of wife’s selection is 3/5.      ( Marks: 5 )

What is the probability that

(a)Both of them will select? 

(b)Only one of them is selected           

(c)None of them is selected

 

Answer:-

Let A and B be the events if the husband’s and wife’s selection, respectively.

Given that P (A) =  and P (B) =

           

(a)the probability that both of them will selected is:

 

(b) The probability that only one of them will be selected is:

 

 

(c) The probability that none of them will be selected is:

 

 

STA301 – Midterm Fall 2019(December)

 

Compute the mean deviation from mean for the following data. (Where = =Mean X 18.6 )

X 14.5 16.5 18.5 20.5 22.5

Frequency 3 5 11 7 3             ( Marks: 5 )

Answer:- Rep

 

How the moment ratios b 1 and b 2 are helpful in determining the shape of a distribution? ( Marks: 3 )

Answer:- (Page 119)

b1 is used to determine the distribution is symmetric or not while b2 is used to determine whether the distribution is positively skewed or negatively skewed.

 

What are the basic properties of random experiment?      ( Marks: 3 )

Answer:- (Page 145)

A random experiment has three properties:

• The experiment can be repeated, practically or theoretically, any number of times.

• The experiment always has two or more possible outcomes. An experiment that has only one possible outcome is not a random experiment.

• The outcome of each repetition is unpredictable, i.e. it has some degree of uncertainty.

 

Write down the principle of least squares method. ( Marks: 2 )

Answer:- (Page 122)

The principle of least squares method is to find the line of best Fit

 

What is the main drawback of grouping process in construction of a frequency table? ( Marks: 2 )

Answer:- (Page 147)

A frequency table has the disadvantage that the identity of individual observations is lost in grouping process.

 

Which two suits of playing cards are made of red color? ( Marks: 2 )

Answer:-

Heart and Diamond are of red color

 

 

 

 

STA301 – Midterm Fall 2012 (December)

1. Write the use of Venn diagram in set theory.        (2 Marks)

Answer:- (Page 134)

The Venn diagrams are used to represent sets and subsets in a pictorial way and to verify the relationship among sets and subsets.

 

2. Can we apply Bayes theorem in the situation where partition of sample space S is created by more than two sets.              (2 Marks)

Answer:-  

Yes we can apply Bayes theorem in the situation where partition of sample space S is created by more than two sets.

 

3. Why the mean of the probability distribution of a random variable X is technically called the Expected value of the random variable X.           (3 Marks)

Answer:- Rep

 

4. in an experiment the stiffness of a spring, the length of the spring under different loads was measured and the regression lines (X on Y and Y on X) were fitted to the model, which gave us the following results:

bxy= 0.67    and      byx= 0.38  (here xy and yx are in the subscript of b)

Calculate the correlation coefficient.                           (3 Marks)

Answer:-

 

5. Assume that X is a number chosen at random from the set of integers between 1 and 14 both inclusive. What is the probability that                                                    (5 Marks)

(i) X is an even number.

Solution:-

Even = 2,4,6,8,10,12,14

P(X=even) = 7/14= ½

 

(ii) X is multiple of 5 or 6.

Solution:-

Multiple of 5 or 6 =5,10,6,12

Probability= 4/14 =2/7

 

6. Find the first two moments about mean from the following data:                   (5 Marks)

X= 34,70,42,54,40,68,56,38,36,72.    

Solution:-

 

X
34	-17	289
70	19	361
42	-9	81
54	3	9
40	-11	121
68	17	289
56	5	25
38	-13	169
36	-15	225
72	21	441

 

 

 

 

 

 

STA301 – Midterm Fall 2021(December)

 

Q#2: for a data set P(A)=0.77,P(B)=0.23 and  find the  and.    ( Marks: 2 )

Answer: 157

P (A∪B) = P (A) + P (B)

= 0.77+0.23

=1

 

 

 

Q#4:Find the data values, calculate person coefficient of skewness using mode of data

0.75,0.89,0.79,0.88,0.99,0.65,0.91,0.59,0.75         ( Marks: 5)

Solution:

Mean = 7.2/9=0.8      Mode = 0.75

X	X2
0.75	0.5625
0.8	0.7921
0.79	0.6241
0.88	0.7744
0.99	0.9801
0.65	0.4225
0.91	0.8281
0.59	0.3481
0.75	0.5625

 

 

 

Q#5: write the two nominal equations of the regression line of X on Y.    ( Marks: 2 )

Answer:- (Page 124)

 

 

 

 

Q#6:A man tossed a fair dice and obtain the following sample space S     ( Marks: 5)

What is the conditional probability that the sum of two die will be 7 given that sum is greater then 6.

 

Solution:

Let A be the event that sum of 7 appears and B be the event the both dice show a number greater than 6 then,

 

Probability= 6/36=1/6

 

 

 

 

 

 

STA301 – Midterm Fall 2012 (December)

 

 

define five number theory?              ( Marks: 2 )

Answer:- (Page 97)

A five-number summary consists of X0,Q1, Median, Q3, and Xm ; It provides us quite a good idea about the shape of the distribution.

 

 

define rule of combination?               ( Marks: 2 )

Answer:- (Page 143)

A combination is any subset of r objects, selected without regard to their order, from a set of n distinct objects.

 

chebycheves theorem inequality find karni the k=2 and k=3 limets of fraction between them btany the?

( Marks: 5 )

Answer:- (Page 94)

a) At least 1-1/22 = 3/4 will fall within 2 standard deviations of the mean, i.e. within the interval

 

b) At least 1-1/32=8/9 of the data-values will fall within 3 standard deviations of the mean, i.e. within the interval      

 

 

 

MIDTERM EXAMINATION (Spring 2012)

STA301- Statistics and Probability

 

Question No. 21

For which type of Data Set Empirical Rule & relationship is applied?  (Marks= 2)

Answer:- (Page 94)

This is a rule of thumb that applies to data sets with frequency distributions that are mound-shaped and symmetric.

 

Question No. 22

If P (A\B) = 0 then A & B are independent. State is it true or false. (Marks = 2)

Answer:-

P (A/B) = P (A) and P (B/A) = P (B). It then follows that two events A and B are independent if and only if

P (A ∩ B) = P (A) P (B) and this is known as the special case of the Multiplication Theorem of Probability.

 

 

 

Question No. 23

X0 = 200, Xm = 500, Q3 = 350

Skewness =?   (Marks = 3)

Answer:- (Page 97)

The distance from X0 to Q1 is equal to the distance from Q3 to Xm.

Therefore it is symmetric

 

Question No. 24

Price (X) = 59,75,27,63,27,28,56

Coefficient of Variation = ?  (Marks = 3)

Answer:-    

 

X	X2
59	3481
75	5625
27	729
63	3969
27	729
28	784
56	3136
Total = 335	18453

 

 

 

Question No. 25

Two dice are rolled, make sample space & also find the probability of Sum is 11 or greater. (Marks : 5)

Answer:-  Rep

 

Question No. 26

Check whether distribution is probability distribution.  (Marks: 5)

 

X	1	2	3	4	5	6	7
P(X)	0.15	0.10	0.20	0.30	0.25	0.075	0.025

 

Answer:- 

TO check whether distribution is probability distribution or not

We have to find two things.

1. 
2. 

Here in Table every P(X) is less than 1 and greater than 0 therefore 1^st condition is satisfied.

Asis not equal to 1 therefore 2^nd condition is not satisfied and it is not a probability distribution.

 

 

 

MIDTERM EXAMINATION (Spring 2012)

STA301- Statistics and Probability

 

When two coins are tossed then what is the probability that at most one head appears.

Answer:-

S = {HH,HT,TH,TT}

A = {HT,TH,TT}

n(S)= 4, n(A)= 3

P(A)= n(A) / n(S)= 3/4

 

2) In how many ways four books can be arranged on shelf?

Answer:-

4! =4x3x2x1 = 24

 

3) when two events are independent, P(A)=0.5, P(B)=0.2 then find P(AnB)=?

Solution: Page 162

P (A ∩ B) = P (A) P (B)

 

4) Define Scatter diagram?

Answer:-     Click here for detail

A scatter plot is a graph made by plotting ordered pairs in a coordinate plane to show the correlation between two sets of data.

 

Q) when two dice are thrown then draw a sample space and find the probability of sum of both dice is 10 (5Marks)

Answer:-    

 

 

Sum of 10 =

Therefore Probability = 3/36

 

 

 

 

 

MIDTERM EXAMINATION (Spring 2012)

STA301- Statistics and Probability

 

1.define sample space

Answer:- (Page 145)

A set consisting of all possible outcomes that can result from a random experiment (real or conceptual), can be defined as the sample space

 

2. What is scatter diagram?

Answer: Rep

 

 

4.caculat coefficient of standard deviation if x=111 123 153 173

Answer:

 

X	X2
111	12321
123	15129
153	23409
173	29929
560	80788

 

S.D

 

MIDTERM EXAMINATION (Spring 2011)

STA301- Statistics and Probability

 

Define complement of an event.(2 marks)

Answer:- (Page 146)

The event “not-A” is denoted by  or Ac and called the negation (or complementary event) of A.

 

What do you know about discrete random variable?(2 marks)

Answer:- (Page 167)

Such a numerical quantity whose value is determined by the outcome of a random experiment is called a random variable. A discrete random variable is one which may take on only a countable number of distinct values

 

How many distinct four-digits number can be performed from the following integers 1,2,3,4,5,6 if each integer is used only once? (3 marks)

Solution:

 

Find the coefficient of variation (C.V) for the following price of a commodity.

Price (X): 8, 13, 18, 23, 30 (5 marks)

Answer:- Rep

 

The following table gives the probability distribution of the random variable X, the number of foreign tours a minister make in a year. (5marks)

X	1	2	3	4	5
P(X)	0.1	0.2	0.3	0.3	0.1

Find the probability that:
1) Minister makes more than 2 and less than 5 tours
2) Minister makes at the most 4 tours

Answer:-

 

 

 

 

 

MIDTERM EXAMINATION (Spring 2011)

STA301- Statistics and Probability

1: what is average and explain it briefly 

Answer: Rep

2: define random experiment

Answer: Page 167
Such a numerical quantity whose value is determined by the outcome of a random experiment is called a

random variable

 

 

 

MIDTERM EXAMINATION (Spring 2011)

STA301- Statistics and Probability

1- why we need to calculate coefficient of variation? (2)

Answer: Rep

2- what is the scatter diagram? (2)

Answer: Rep

3- A number X chosen at random from the integers 1 to 14 both are inclusive. find the probability
i) if x is an even number
ii) if x is an multiple of 5 or 6 (5)

Answer: Rep

4- P(A/B) = P(B/A) if P(A) = P(B) is the statment true or wrong if statment is not true then justify the reason? (3)

Answer: Rep

MIDTERM EXAMINATION (Spring 2011)

STA301- Statistics and Probability