Solve your IGNOU Doubts

Question:

In order to compare the mileage yields of 3 kinds of Gasoline, several tests were run, and the following results were obtained:

Gasoline A:	19	21	20	18	21	21
Gasoline B:	23	20	22	20	24	23
Gasoline C:	20	17	21	19	20	17

Carry out the Analysis of Variance test and test whether there is significant differences between the average mileage of 3 kinds of gasoline at 5% level of significance.

See Answer →

Question:

In a population of size N = 5, the values of the population characteristics are 1, 3, 5, 7, 9, a sample of size 2 is drawn. Verify that $\bar{y}$ is an unbiased estimate of $\bar{Y}$ andV( $\bar{y}$ ) is equal to

$\bg_white V(\bar{y})=\frac{N-n}{Nn}S^2.$

See Answer →

Question:

A population consists of 10 villages with a total of 212 households. The second column of the accompanying table shows the number of households corresponding to each village. Select a PPS with replacement sample of 6 villages by using the Cumulative Total method:

Village	1	2	3	4	5	6	7	8	9	10
No. of Households	35	28	20	25	30	19	10	12	18	15

See Answer →

Question:

A sample of 100 employees is to be drawn from a population of collages A and B. The population means and population mean squares of their monthly wages are given below:

Village	Ni	$\bar{X_i}$	$S_{i}^{2}$
Collage A	400	60	20
Collage B	200	120	80

Draw the samples using Proportional and Neyman allocation techniques and compare. Obtain the sample mean and variances for the Proportional Allocation and SRSWOR for the given information. Then Find the percentage gain in precision of variances of sample mean under the Proportional Allocation over the that of SRSWOR.

See Answer →

Question:

State whether the following statements are true or false and also give the reason in support of your answer:

(a) $V_{opt}\left ( \bar{X_s_t} \right )$ lies between $V_{prop}\left ( \bar{X}_{st} \right )$ and. $V_{Random}\left ( \bar{X}_{st} \right ).$ prop st Random st

(b) The total number of all possible samples of size 3 without replacement from a population of size 7 is 21.

(d) In a Two-way Analysis of Variance test with 5 observations per cell having 4 blocks and 4 treatments the degree of freedom for the total variation is 64.

(e) The probability of selection of a sample of n from the population by SRSWOR is 1/ N.

See Answer →

Question:

A hospital specialising in heart surgery. In 2022 total of 2000 patients were admitted for treatment. The average payment made by a patient was Rs 1, 50,000 with a standard deviation of Rs 25000. Under the assumption that payments follow a normal distribution, answer the following questions.
(i) The number of patients who paid between Rs 1,40,000 and Rs 1,70,000.
(ii) The probability that a patient bill exceeds Rs 1,00,000.
(iii) Maximum amount paid by the lowest paying one-third of patients

See Answer →

Question:

If X ~ Gamma , and Y ~ Gamma , (θ α) (θ β) be two independent gamma distributions and

$U=\frac{X}{X+Y}$ and $V=X+Y$ then find the distribution of U.

See Answer →

Question:

Explain the procedure of assigning probability in a continuous world of probability theory

See Answer →

Question:

Let (Ω, $F,P$ , ) be a probability space and $X_1,X_2,X_3,..$ be a sequence of independent and identically distributed (i.i.d.) random variables from the uniform distribution on the interval [12, 20]. If Xn denotes the sample mean of the first n random variables of the sequence

$X_1,X_2,X_3,...,$ and $\bar{X}_n\overset{p}{\rightarrow}a.$ Find the value of a.

See Answer →

Question:

In an election there are two candidates. Being a statistician, you are interested in predicting the result of the election. So, you plan to conduct a survey. Using the learning skill of this course answer the following question. How many people should be surveyed to be at least 90% sure that the estimate is within 0.03 of the true value?

See Answer →

Question:

In the study learning material (SLM), you have seen many situations where Poisson distribution is suitable and discussed some examples of such situations. Create your own example for a situation other than those that are discussed in SLM. If you denote your created random variable by X then find the probability that X is less than 2.

See Answer →

Question:

Suppose two friends Anjali and Prabhat trying to meet for a date to have lunch say between 2 pm to 3 pm. Suppose they follow the following rules for this meeting:

• Each of them will reach either on time or 10 minutes late or 20 minutes late or 30 minutes late or 40 minutes late or 50 minutes late or 1 hour late. All these arrival times are equally likely for both of them.

• Whoever of them reaches first will wait for the other to meet only for 10 minutes. If within 10 minutes the other does not reach, he/she leaves the place and they will not meet.

Find the probability of their meeting.

See Answer →

Question:

Evaluate the integral $\int_{0}^{4}\frac{dx}{\sqrt{4x-x^2}}$ using beta and gamma functions.

See Answer →

Question:

Evaluate the integra $\iint_{D}^{}e^{4x+5y}dx\,dy,$ where D= $\left \{ \left ( x,y \right ):x\geq 0,y\geq 0,x+y\leq1 \right \},$ by considering D as a region of Type I and then as a region of Type II

See Answer →

Question:

If f :[0, 5] → $\mathbb{R}$ be a function defined by $f(x)=x^2+2x+1,\,x\in$ [0, 5]. Show that f is Riemann integrable using both definitions. Also, verify that the results of both definition match.

See Answer →

Question:

Test the convergence of the series $\frac{3}{5.9.7}X+\frac{5}{10.12.11}X^2+\frac{7}{15.15.15}X^3+\frac{9}{20.18.19}X^4+...,X>0.$

See Answer →

Question:

Give an example of a set which is convex but not affine. Justify your claim with a proper explanation.

See Answer →

Question:

Find the equation of a line passing through points A(2, 3, 5) and B(5, 8, 9). Also, find the coordinates of a point on this line which is at a distance of 10 units from point A opposite to the side of point B.

See Answer →

Question:

In R we have a built-in data set “trees”. A screenshot of the first four rows together with the R code to obtain it is given as follows. To get more detail about this data set you can run ?trees command on R console.

Image ignouassignments-ignouacademy-com--p-solve-77207

Note that all the three variables of this data set are numeric. So, assuming each row of this data set is a point in 3-dimension. Find the distances between the points corresponding to the first and the third rows using the Manhattan and Chebyshev distance formula.

See Answer →

Question:

A ball is thrown in an upward direction. If the variable x represents the velocity of the ball when it strikes the ground. Classify variable x as discrete or continuous. Justify your answer with a proper explanation.

See Answer →