Let Y Be a Bernoulli Random Variable with Success Probability $\hat { p }$

question 60

Essay

Let Y be a Bernoulli random variable with success probability Pr(Y = 1)= p, and let Y₁,..., Y_n be i.i.d. draws from this distribution. Let $\hat { p }$ be the fraction of successes (1s)in this sample. In large samples, the distribution of $\hat { p }$ will be approximately normal, i.e., $\hat { p }$ is approximately distributed N(p, $\frac { p ( 1 - p ) } { n }$ ). Now let X be the number of successes and n the sample size. In a sample of 10 voters (n=10), if there are six who vote for candidate A, then X = 6. Relate X, the number of success, to $\hat { p }$ , the success proportion, or fraction of successes. Next, using your knowledge of linear transformations, derive the distribution of X.

---

Definitions:

Property Value

The monetary worth of a piece of real estate, which can be affected by factors such as location, condition, and market trends.

Swimming Pool

A man-made basin filled with water designed for swimming or leisure activities.

Reliance

Reliance refers to the act of depending or counting on someone or something, often in the context of legal contracts where one party's actions are based on the promises or agreements made by another.

Donee Beneficiary

A party who benefits from a contract made between two other parties, without any obligations to perform or pay.