Education: MTH - 302 ETE QUESTIONS

MTH - 302 ETE QUESTIONS (TEXT BASED)

Q 1 :: If the variance for the random variable x is 19 and the second moment about the origin is 100 then the first moment about the origin is-

Q .2 :: In an examination 40 percent students have failed in mathematics, 25 percent of the students have failed in chemistry and 10 percent have failed in both mathematics and chemistry. A student is selected at random. What is the probability that the student has failed in mathematics if it is known that he has failed in chemistry?

0.50

0.20

0.40

0.60

Q . 3 :: If the first moment about the origin for the random variable x is 10 and the variance is 0 then the second moment about the origin is-?

100

Q. 4 :: A language class has only 3 students A,B and C and they independently attend the class. The probabilities of the attendance of A, B and C on a given day are 1/2, 1/3 and 3/4 respectively. Find the probability that the total number of attendance in 2 consecutive days is exactly 3.

1/3

2/3

3/8

1/24

Q . :: If the letters of the word ‘VOWELS’ be arranged at random, what is the probability that there are exactly two letters between E and O?

1/4

1/3

1/6

1/5

Q. : If the letters of the word ‘VOWELS’ be arranged at random, what is the probability that there are exactly two letters between E and O?

1/4

1/3

1/6

1/5

Q .:: A fair die is rolled. The probability of getting an even face given that face is less than 5 is given by:

0.5

0.6

0.8

Q . Which one of these variables is a continuous random variable?

The time it takes a randomly selected student to complete an exam.

The number of tattoos a randomly selected person has.

The number of women taller than 68 inches in a random sample of 5 women.

The number of correct guesses on a multiple choice test.

If a problem in Statistics is given to three studentswhose chances of solving it are 1/3, 2/3, 1/2 respectively.Then the probability that the problem is solved if all of the three students try independently is:

1/2

3/8

1/9

8/9

A random sample {x1, x2,...,xn} is taken from a normalpopulation N(μ,1). Then

1nΣi=1nxi2 is an unbiased estimator of

μ^2+1

μ^2

μ^2−1

A machine that winds steel cables for bridges averages three snags per mile of cable. If a bridge requires 0.26 mile of cable, what is the probability of no snag? (Given e-3= 0.15 and e-0.78= 0.46)

0.225

0.046

0.15

0.46

If F(x)=x3 is the distribution function and f(x) is the p.d.f. of a continuous random variable ’X’ in the interval [0,1], then f(x)=?

3x^2

x^4/4

x^2

None of these

If x is the random variable and the first and second moment about the origin are 20 and 4 respectively then the variance is

0.6

If X is a Poisson variate with mean =10. then what is the probability of x=5 trial

0.03783

0.5

0.68676

If V(T1) =0.1 and V(T2)=0.001 then which one between T1 and T2 is less efficient

Both are equally efficient

We can't predict the efficiency based on the the given information

Find the parameters of the binomial distribution with mean 48 and the standard deviation 4?

n = 72 and p = 1/3

n = 144 and p = 1/3

n = 144 and p = 2/3

n = 72 and p = 2/3

In a Binomial distribution with 6 independent trials, the probabilities of 3 and 4 successes are found to be 0.2457 and 0.0819 respectively. Find the parameter p of the binomial?

4/13

5/9

4/9

8/13

(QQ) In a binomial distribution consisting of 6 independent trials, the probability of 3 and 4 successes are 0.2457 and 0.0819 respectively. The parameter p of the binomial?

(QQ) If a coin is tossed 4 times then the probability of getting at most 3 heads is:

15/16

10/16

12/16

5/16

(QQ) If ‘X’ is a binomial variate with parameter ‘p’ such that n=6 and P(X=0)=0.5 and P(X=1)=0.25, then ‘q’=?

12/13

1/13

1/6

1/7

(QQ) The average number of customers who appear at a counter of a certain bank per minute is two. Find the probability that during a given minute one or more than one customers appear? (Given e-2 = 0.135)

0.27

0.865

0.676

0.15

(QQ) Which of the following is correct?

V(X)=E[{X-E(X)}2]

V(X)=[E(X)]2-E(X2)

V(X)= E[X-E(X)]

V(X)=[X-E(X)]2

(QQ) In a Binomial distribution with 6 independent trials, the probabilities of 3 and 4 successes are found to be 0.2457 and 0.0819 respectively. Find the parameter p of the binomial?

4/13

5/9

4/9

8/13

(QQ) If a coin is tossed 4 times then the probability of getting at most 3 heads is:

15/16

10/16

12/16

5/16

(QQ) If ‘X’ is a binomial variate with parameter ‘p’ such that n=6 and P(X=0)=0.5 and P(X=1)=0.25, then ‘q’=?

12/13

1/13

1/6

1/7

(QQ) If a random variable follows Poisson distribution such that P(X=1) = P(X=2). Find the mean and variance of the distribution?

Mean = 2 and Variance = 4

Mean = 2 and Variance = 2

Mean = 4 and Variance = 6

Mean = 4 and Variance = 4

(QQ) In a Binomial distribution with 6 independent trials, the probabilities of 3 and 4 successes are found to be 0.2457 and 0.0819 respectively. Find the parameter p of the binomial?

4/13

5/9

4/9

8/13

0.27

0.865

0.676

0.15

(QQ) Find the parameters of the binomial distribution with mean 48 and the standard deviation 4?

n = 72 and p = 1/3

n = 144 and p = 1/3

n = 144 and p = 2/3

n = 72 and p = 2/3

(QQ) Which of the following is not an assumption of Binomial Distribution?

There are only two disjoint outcomes

The number of trials must be finite.

Trials are independent

Trials are dependent.

(QQ) Consider the statistic T and if E(T2)= 600 and V(T)=25 then the T is unbiased of

(QQ) Which of the following is correct?

Options Are-

V(X)=E[{X-E(X)}2]

V(X)=[E(X)]2-E(X2)

V(X)= E[X-E(X)]

V(X)=[X-E(X)]2

(QQ) If V(T1) =0.2 and V(T2)=0.002 then which one of the estimator between T1 and T2 is best

Both are equally efficient

We can't predict the efficiency based on the the given information

(QQ) which one of the statements below is correct?

If the significance level is equal to 0.1, it implies that we are

10% confident that the population mean will lie between the confidence limits

If the sample size increases the confidence interval becomes wider.

As the population standard deviation increases, the confident interval becomes narrower.

A 90% confidence interval for the population mean is narrower than a 95% confidence interval for the population mean.

0.27

0.865

0.676

0.15

(QQ) In a sample of 9 observations, the sum of square of items from mean was 80.96. In another sample of 10 observations , the value was found to be 108.9. Test whether the difference in variance is significant at 5% level. Given F(8,9) = 3.18, F(9,8) = 1.15.

Ho is accepted that the difference is not significant.

Ho is rejected that the difference is not significant.

Ho is accepted that the difference is significant.

Ho is rejected that the difference is significant.

(QQ) Which of the following is correct for Chi Square-test forgoodness of fit?

Sum of the expected frequencies < Sum of the observedfrequencies

Sum of the expected frequencies > Sum of the observedfrequencies

Sum of the expected frequencies = Sum of the observedfrequencies

Sum of the expected frequencies = 2(Sum of the observedfrequencies)

(QQ) In a sample of 8 observations, the sum of square of items from mean was 84.4 and mean is 72. In another sample of 10 observations , the value was found to be 102.6 and mean 68. Test whether the difference in mean is significant at 5% level. Given table value of t at 16 d.o.f is 3.07.

Hois accepted that the difference is not significant.

Ho is rejected that the difference is not significant.

Ho is accepted that the difference is significant.

Ho is rejected that the difference is significant.

(QQ) Consider the statistic T and if E(T)= 5 and V(T)=0.05 then the T2 is unbiased of

25.05

5.05

24.05

(QQ) One problem with hypothesis testing is that a real effect may not be detected. This problem is most likely to occur when

the effect is small and the sample size is small.

the effect is large and the sample size is small.

the effect is small and the sample size is large.

the effect is large and the sample size is large.

(QQ) If a coin is tossed 4 times then the probability of getting at most 3 heads is:

15/16

10/16

12/16

5/16

(QQ) To fit a non-linear curve Y=a+bX+cX2 to a data, which of the following sums is not required?

Sum of the values of variable ‘X^2’

Sum of the values of variable ‘Y’

Sum of the values of variable ‘XY’

Sum of the values of variable ‘Y^2’.

(QQ) Two samples of sizes 25 and 35 are independently

drawn from two normal populations, where the unknown

variances are assumed to be equal. The number of degrees

of freedom for the equal-variances t-test statistic is:

(QQ) If V(T1) < V(T2) then T1 is

Unbiased

Efficient

Sufficient

Consistent

(QQ) In a locality of 20000 families a sample of 900 families

was selected at random. Of these 900 families 250 families

were found to have a monthly income of Rs.500 or less. Find

the probable limit of proportion for the families having a

monthly income of Rs.500 or less?

Options Are-

0.20 to 0.29

0.129 to 0.411

0.359 to 0.288

0.27 to 0.73

(QQ) A random sample of recorded deaths in a city in India

during the last year showed an average life span of 70

years. Does the average life span today is equal to 68 years

with a standard deviation of 0.75. Use 5% level of

significance.

Options Are-

Ho is expected and concluded that average life span today is greater than 68 years.

Ho is rejected and concluded that average life span today isgreater than 68 years.

Ho is rejected and concluded that average life span today isnot equal to 68 years.

Ho is expected and concluded that average life span todayis equal to 68 years.

(QQ) Consider the statistic T and if E(T2)= 600 and V(T)=25 then the T is unbiased of

Options Are-

(QQ) In a one-tail test for the population mean, if the null

hypothesis is not rejected when the alternative hypothesis is

true, then:

Type I error is committed

Type II error is committed

a correct decision is made

OPTION a two-tail test should be used instead of a one-tail test

(QQ) If the variance of three estimators A, B, and C are given as

Options Are-

V(A) =0.1, V(B) =0.01, and V(C) =0.001 then

Estimator A is better than B and C

Estimator B is better than A and C

Estimator C is better than B and A

Estimator A is better than B

(QQ) If for the n=4 data,

Σx = 19 Σy = 24 ΣX2 = 20.75 ΣY2 = 26 and

the coefficient of correlation is 0.9902

then ΣXY =?

Options Are-

Its not available in the option

(QQ) Which of the following statements correctly describes

a difference between the F and t distributions?

Options Are-

The F distribution is discrete, the t distribution is continuous

The t distribution is valid only for positive numbers, the F for

all real values

The F distribution is symmetrical, the t distribution is

skewed to the right

The F distribution is valid only for positive numbers, the t for

all real values

(QQ) If b(X,Y) is regression coefficient of X on Y, r(X,Y) is

correlation coefficient and S.D.(X) is standard deviation in X

then b(X,Y)=?

r(X,Y)/S.D.(X)

r(X,Y) /S.D.(Y)

r(X,Y)/[S.D.(X)*S.D.(Y)]

[r(X,Y)*S.D.(X)]/S.D.(Y)

(QQ) In a random sample of 300 persons of a town, 180 are

found to be tea drinkers. In a sample of 500 persons from

another town, 200 are found to be tea drinkers. What is the

standard error?

Options Are-

0.04

0.072

0.051

0.088

(QQ) If ‘X’ is a binomial variate with parameter ‘p’ such that

n=6 and P(X=0)=0.5 and P(X=1)=0.25, then ‘q’=?

Options Are-

12/13

1/13

1/6

1/7

(QQ) What should you conclude if the two lines of regression

(y on x, and x on y) are perpendicular to each other?

Options Are-

The correlation coefficient =0

The correlation coefficient =1

The correlation coefficient =-1

No conclusion can drawn

(QQ) If V(T1) =0.2 and V(T2)=0.002 then which one of the

estimator between T1 and T2 is best--------

Options Are-

Both are equally efficient

We can't predict the efficiency based on the the given

information

(QQ) Which of the following is not an assumption of Binomial

Distribution?

Options Are-

There are only two disjoint outcomes

The number of trials must be finite.

Trials are independent

Trials are dependent.

(QQ) From the 16 data, the calculated mean is 100 and the

standard deviation is 5. If the hypothesis mean is 95 Then

the calculated t-test value is---

Options Are-

data is insufficient

(QQ) From the regression line 16x=9y 94, find the regression

coefficient x on y?

ANS-?

(QQ) Which of the following is a necessary condition for

using a t distribution table?

n is small

s is known but σ is not

the population is finite

(a) and (b) but not (c)

(QQ) If the regression coefficient of x on y is-1/6 and that of y

on xis-3/8, find the correlation coefficient between x and y?

ANS-?

(QQ) What is our decision for a goodness-of-fit test with a

computed value of chi-square of 1.273 and a critical value of

13.388?

Options Are-

Do not reject the null hypothesis

Reject the null hypothesis

Unable to reject or not reject the null hypothesis based on data

Should take a larger sample

(QQ) A random sample of recorded deaths in a city in India

during the last year showed an average life span of 70

years. Does the average life span today is equal to 68 years

with a standard deviation of 0.75. Use 5% level of

significance.

Options Are-

Ho is expected and concluded that average life span today

is greater than 68 years.

Ho is rejected and concluded that average life span today is

greater than 68 years.

Ho is rejected and concluded that average life span today is

not equal to 68 years.

Ho is expected and concluded that average life span today

is equal to 68 years.

(QQ) From the two regression line from certain data,

calculate coefficient of correlation:

16x=4y +16 and 4y=9x-8

ANS-?

(QQ) If r = 0.6, byx = 1.2 then bxy = ?

Options Are-

0.3

0.2

0.72

0.40

Education

Tuesday, July 5, 2022

MTH - 302 ETE QUESTIONS

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