be two independent gamma distributions and
then find the distribution of U.
# Solution We do the change of variables $(X,Y)\mapsto(U,V)$ with $$ U=\frac{X}{X+Y},\qquad V=X+Y. $$ Invert: $$ X=UV,\qquad Y=(1-U)V, $$ with domain $0
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be two independent gamma distributions and
then find the distribution of U.
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 arrive either on time or 12 minutes late or 24 minutes late or 36 minutes late or 48 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.
(b) 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.
Explain the procedure of assigning probability in the discrete world of probability theory.
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?