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.
### Example Situation for Poisson Distribution Suppose a call center receives an average of 3 customer calls per hour. We define the random variable: \[ X = \text{"Number of customer calls received per hour"} \] Since calls arrive randomly and independently, \(X\) follows a Poisson distribution with mean (rate parameter) \( \lambda = 3 \). That is: \[ ____ _______ _________ ___ __________ ___ __________ ________ ___.
___ ___ _____ __________ _____.
________ ______ _____ ____ ________ ______ _______ ____ ________ _______ ______.
___ ______ ____ _________ ___ __________ _________ _________ ___ ___ ___ _________.
______ ______ _________ _____ ________ ______ ________ _______.
_____ ___ _______ ______ _______.
__________ ________ _________ __________ __________.
______ ______ __________ _____ _________ _________ _________ ________.
______ _____ __________ __________ _________ _______ _______ __________.
__________ _______ _________ _____ ___ ____ __________ ______ ____ ___ ____ ______.
___ ________ _____ _________ ___ ______ ___ _________ ____ ____.
___ ____ ________ ___ __________ _________ ___ ________.
___ _______ ____ ___ ___ ____ ____ ____ _____ _____ ______.
________ ___ _____ _______ __________ ______ ________ ___ _________ ________ ____.
_________ ________ ________ _______ ________ _______ _______.
______ __________ __________ _____ _______ ________ ___.
___ ___ _______ _______ ____ _______.
______ ___ ________ ________ ____.
___ ___ ___ ______ _________.
____ ______ _______ _________ _____ ____ _____ ______ ______.
__________ ___ _______ _________ ________.
____ ____ _____ ______ ___ __________ ______ ____.
________ ________ _________ ____ ______ _________ _______ ________ _____ ________ _____.
____ ____ ___ ___ ____ _______ __________ __________.
_______ _____ ____ ________ ____ _________.
_______ ____ _________ ___ __________ __________ _________ ____ _________.
____ __________ __________ ________ _______ ____ __________ ________ ________ _____.
_______ _______ ____ _______ _______ _________ __________.
_____ ____ ___ ________ _____ _______ ___ _________ _____.
Get Full Answer on WhatsApp
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?
If is a sequence of continuous random variables such that:
then prove that .
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.
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.
Explain the procedure of assigning probability in a continuous world of probability theory.
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.
If and
are two independent gamma distributions and
then find the distribution of .