Birthday Paradox:
The problem is to find that how many people must be there in a room for having same birthday.
Than what is paradox in it? Paradox is that you may think that the possibility will only come when there are many (lets say 365) people in the room. But you will see that the probability will occur even for few people.
To solve this problem we index the total number of the people in the room as
1,2,3….k where k is equal to the total number of people in room.
And also let us assume that all years has 365 days (ignoring the issue of leap years). Lets say n=365 days
For
i=1,2,3,…,k let bi be the day on which the birthday of ith person occurs, assuming 1< bi
Analysis Using Indicator Variable: Now we will use indicator variable to calculate an approximately simpler solution to this problem i.e. birthday paradox. We define, for each pair of people (i , j) in the room out of total people k, let us define an indicator variable: Xij indicator random variable, for 1< i < j < k so, Xij = I (person i and j having the same birthday) = Now applying expectancy on both side of the above equation, we have E(Xij) = Pr (person i and j having the same birthday) = 1/n (as calculated previously) So, for the total, say X be the random variable that counts total number of pairs having same birthday. X = ∑_(i=1)^k ∑_(j=i+1)^k Xij Taking expectations on both sides, we get E (X )=E ( ∑_(i=1)^k ∑_(j=i+1)^k Xij ) = ( ∑_(i=1)^k ∑_(j=i+1)^k E (Xij) Solving the summation mathematically we get E (X )= k(k-1)/2n If k(k-1) > 2n than the number of expected pairs having birthday on the same day will may be greater or equal to one. Solving k(k-1) > 2n we get: r = √2n + 1 Now, for example if we have n=365 and k=28 we get by using equation k(k-1)/2n => 28(27)/2(365) =1.0368 Thus with 28 people in the room and 365 days in a year we get one pair of people having birthday on the same
The ancient Babylonian calendar was rather similar to our modern calendar today. All together, the Babylonian calendar had a total of 12
The Monty Hall problem is a hallmark of modern statistics. It was first officially published in the “Ask Marilyn” column of Parade magazine, in which the world's highest IQ, Marilyn vos Savant, answered reader questions and solved an enormous variety of puzzles and riddles. The Monty Hall problem was sent in by a reader and published exactly as follows:
The setting of this observation takes place in a suburban home in southern Maryland. The home belongs to the grandmother of the subject. The day is before thanksgiving and there are a lot of family members present. Six people other than Imani are here; her older brother who seemed to be 2 years old, her male cousin who seems to be the same age as her, her grandmother, two aunts, an uncle, and her mother. There are three boys total and four females, including Imani. The home has three floors, with most of the activity taking place in the kitchen and family room. In the family room, there were couches, a tread mill, television, and a set of steps that lead to the kitchen. The kitchen has a table, an island, appliances,
3.After 2 minutes, each participant in both groups will get a clothespin. Each person is going to count the maximum number of times they can squeeze the clothespin in one minute.
The Maya elite developed a complicated calendar system. There are two main cycles in their calendar; one was made up of 260 days and the other 365. Each day is named from both the 260 and 365-day calendars. Because of this each full day name could only repeat every 18,980 days or once every 52 years.
Like I mentioned above, your room will likely be dark but PBPs will use that to their advantage and will know which angles are more tasteful than others. Regardless, you are still worth having high-quality photography to hold onto and look at each new birthday. You might appreciate being reminded of the best day of your life.
two or more people; this is something that we do all the time. It is
n hypothesis of the experiment is that the group containing four members will perform better than the group containing two members. This is the foundation from which we have conducted our experiment.
This cultural event also had a religious meaning and ceremony that went along with it. Like traditional ways, the birthday girl has to attend a special Mass that includes her close friends a...
Moira’s Birthday party is a funny book full of chaos and fun. The book starts with Moira asking her parents for a birthday party. She wants to invite grades k-6 to her party but her parents say that's too many and to only invite six kids. She goes to school the next day and gets cared away and invites k-6 but doesn't tell her parents. On her birthday six kids show up and her parents start the party but soon 100 more kids show up. Her parents freak out and start worrying about how to feed all the kids. Moira comes up with an idea to feed them all. She calls the pizza place and a bakery and asks for 100 of each. They say that's impossible and can only do six, so they sent them six. This isn't enough to feed all the kids, so the kids go and bring
Birthday Party, a short story written by Katherine Bush in 1946 explores the topic of marriage and its repercussions. Katherine Bush showcases the idea of an individual's involvement in an unloving and abusive marriage lead to the victims lead to despair and unhappiness. The theme of the short story is developed through the use of extended metaphors. The wife, who is the victim of the husband’s verbal abuse attempts to hide her sadness from the outside world and her “big hat” is a metaphor for this statement. Similar to how no one else is unaware of her sadness, the big hat covers her face and she goes unnoticed by many. The narrator states that she witnesses the woman “[c]rying quietly and heartbrokenly and hopelessly, all to herself, under the gay brim of her
“The Lottery”, by Shirley Jackson is a short story about a disturbing social practice in a village. Besides, there were about three hundred citizens in the small village where the setting took place. The introduction of “the lottery” is about an event that takes place every year on 27th in the month of June, where the community members of this tradition organize a lottery. Everyone in the village including small children to adults is expected to participate. Besides, when this story was introduced at the very first in 1948 by Shirley Jackson, many people were upset. This is because this story was so strange to undertake in modern enlightened times.
Everyone from the town-- men, women and children-- gather to put a list of family names within the village into a black lottery box. Everyone in the village has their jobs on the
The reason we use this formula in particular is because the birthdays of 30 random people in a room are all independent events that do not rely on one another for it’s occurrence.
Then, to work out the total no. I added up all the numbers in the