Binomial Distribution Homework: Equations and Solutions

WxlaXZlcyBhIEN1cnJlbnRQb3dlcmVkIGFuZCB0aGUgY2l0eSBmb3IgZSB7eS9vLm8vcHV1LnNoL2VwbG0=[/quote]In summary, the conversation is about a formula for calculating the probability of a certain value in a given range, and finding the formula for standard deviation. The conversation includes a link to a problem and a request for help.
  • #1
planauts
86
0

Homework Statement


http://puu.sh/epl6
Answer
http://puu.sh/eplm


Homework Equations





The Attempt at a Solution


No clue on how to attempt this problem. Any help would be appreciated, thanks!
 
Last edited by a moderator:
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  • #2
planauts said:

Homework Statement


http://puu.sh/epl6
Answer
http://puu.sh/eplm


Homework Equations





The Attempt at a Solution


No clue on how to attempt this problem. Any help would be appreciated, thanks!

(a) What is the formula for [itex] f(k) \equiv \Pr\{X = k|X \geq 2 \},[/itex] for k = 2, 3, ...,n? Then [itex] E(X | X \geq 2) = \sum_{k=2}^n k f(k), [/itex] and you ought to be able to get the cited formula from this.
(b) What is the formula for σ in terms of n and p? Look at it carefully.

RGV
 
Last edited by a moderator:

1. What is the binomial distribution?

The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials with a given probability of success.

2. How do you calculate the probability of a specific number of successes in a binomial distribution?

The probability of a specific number of successes (k) in a binomial distribution can be calculated using the formula P(k) = nCk * p^k * (1-p)^(n-k), where n is the number of trials, p is the probability of success, and nCk is the combination function.

3. What is the difference between a binomial and a normal distribution?

A binomial distribution is used for discrete data, while a normal distribution is used for continuous data. Additionally, a binomial distribution has a fixed number of trials and a probability of success, while a normal distribution has a mean and standard deviation.

4. How do you find the mean and standard deviation of a binomial distribution?

The mean of a binomial distribution is given by np, where n is the number of trials and p is the probability of success. The standard deviation is given by √(np(1-p)).

5. Can the binomial distribution be used for real-world data?

Yes, the binomial distribution can be used to model real-world data that can be categorized as success or failure in a fixed number of trials with a known probability of success. Examples include flipping a coin, rolling a die, or testing the effectiveness of a new drug.

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