Solve your IGNOU Doubts

Question:

Using the generating function, establish the relation between H_n(x) and H_n(-x).

See Answer →

Question:

A hospital specializing in heart surgery. In 2022, a 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. 25,000. 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). The maximum amount paid by the lowest-paying one-third of patients.

See Answer →

Question:

If $X \sim \text{Gamma}(\alpha, \lambda)$ and $Y \sim \text{Gamma}(\beta, \lambda)$ are two independent gamma distributions and

$U = \frac{X}{X + Y}, \quad V = X + Y$

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:

If $X_1, X_2, X_3, X_4, \dots$ is a sequence of continuous random variables such that:

$f_X(x) = \frac{n}{2} e^{-n|x|}$

then prove that $X_n \xrightarrow{P} 0$ .

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 which 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:

A spherical balloon is being Inflated at the rate of 900 cm³/sec. How fast is the Radius of the balloon Increasing when the Radius is15 cm.

See Answer →

Question:

Suriti wants to Invest at most 12000 in saving certificates and National Saving Bonds. She has to invest at least 2000 in Saving certificates and at least 4000 in National Saving Bonds. If Rate of Interest on saving certificates is 8% per annum and rate of interest on national saving bond is 10% per annum. How much money should she invest to earn maximum yearly income? Find also the maximum yearly income.

See Answer →

Question:

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

See Answer →

Question:

Show that

i) $\lim_{n\to 0}\frac{|x|}{x}\text{does not exist.}$

ii) $f(x)=|x|\text{is continuous at}x=0.$

See Answer →

Question:

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

See Answer →

Question:

If m times the m^th term of an an A.P. is n^th times its nth term, show that (m + n)^th term of the A.P. is zero.

See Answer →

Question:

If f: [0, 5]→ R be a function defined by f(x) = x²+2x+1, x ∈ [0, 5]. Show that f is Riemann integrable using both definitions. Also, verify that the results of both definition match.

See Answer →

Question:

Find the inverse of the matrix A = $\begin{pmatrix}1&6&4\\2&4&-1\\-1&2&5\end{pmatrix}$ , if it exists, -1 2 5