a) Suppose two friends Anjali and Prabhat trying to meet for a date to have lunch say between 1 pm to 2 pm. Suppose they follow the following rules for this meeting:
Each of them will arrive 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.
The situation can be modeled using the framework of discrete probability distributions where both individuals independently choose their arrival times from a finite set of equally likely outcomes. Let us define the possible arrival times in minutes after 1 pm as 0, 10, 20, 30, 40, 50, and 60. Thus, each of them has 7 possible choices, and since all these choices are equally likely, the probability of each arrival time is ( \frac{1}{7} ). Because the arrival times of Anjali and Prabhat are independent, the combined sample space consists of all ordered pairs of these times, giving a total of ( 7 \times 7 = ______ _________ _____ _______ __________ _______ ____ ___ ____.
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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 95% sure that the estimate is within 0.05 of the true value?
a) Suppose two friends Anjali and Prabhat trying to meet for a date to have lunch say between 1 pm to 2 pm. Suppose they follow the following rules for this meeting:
Each of them will arrive 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.
Explain the procedure of assigning probability in the discrete world of probability theory.
If and
be two independent gamma distributions and
and
then find the distribution of V.
Solve the problem in part (a) simply by replacing 10 minutes by 5 minutes all other things are the same.