Solve your IGNOU Doubts

Question:

If X ~ Gamma , and Y ~ Gamma , ( $\alpha \beta$ ) be two independent gamma distributions and $U=\frac{X}{X+Y}$ and V = X+ Y then find the distribution of U.

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Question:

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

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Question:

If X₁,X₂,X_3,X₄,........be a sequence of continuous random variables such that f_x2(x)= $\frac{n}{2}$ $e^{-nx}$ then prove that

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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?

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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 which are discussed in SLM. If you denote your created random variable by X then find the probability that X is less than 2.

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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.

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Question:

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

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Question:

Evaluate the integral $\int \int e^{4x+5y}$ dx dy, where D = $\left \{ (x,y) : x \geq 0, y \geq 0, x+y\leq 1 , \right \}$ by considering D as a region of Type I and then as a region of Type II.

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Question:

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

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Question:

Test the convergence of the series

$\frac{3}{5.9.7}x +\frac{5}{10.12.11}x^{2}+\frac{7}{15.15.15}x^{3}+\frac{9}{20.18.19}x^{4}+........,x>0.$

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Question:

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

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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.

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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.

> head(trees,4)

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.

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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.

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Question:

Business environment risk index

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Question:

Currency derivatives market in India

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Question:

Repurchase agreements

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Question:

International money transfer mechanism