# Suppose x is a discrete, binomial random variable

• nachelle
In summary, to calculate P(x > 2) for a binomial random variable with n = 8 and p = 0.3, we can use the formula P(x > value) = 1 - P(x <= value), where P(x <= value) can be found using the binomial distribution formula. This involves calculating the sum of all values of x up to and including the desired value, in this case x = 2. The final answer will depend on the specific values of n and p given.
nachelle
How do I do this p(x<1) this sign has a _ under the <
n=6 p=0.1

Suppose x is a discrete, binomial random variable.

Calculate P(x > 2), given trails n = 8, success probability p = 0.3

[Hint: P(x > value) = 1 – P(x <= value) <= is a < with a _ under it

(tell me the number value you get)

nachelle said:
How do I do this p(x<1) this sign has a _ under the <
n=6 p=0.1
Suppose x is a discrete, binomial random variable.
Calculate P(x > 2), given trails n = 8, success probability p = 0.3
[Hint: P(x > value) = 1 – P(x <= value) <= is a < with a _ under it
(tell me the number value you get)

A binomial random variable distribution is given by $$f(x)=\left( \begin{array}{c} n \\ x \end{array} \right) p^x (1-p)^{n-x}$$. That's a starting point.

Edit: one more hint - the probability that a discrete random variable will have a value less or equal x is $$F(x) = P(X \leq x) = \sum_{i;x_{i}\leq x}f(x_{i})$$.

Last edited:
nachelle said:
How do I do this p(x<1) this sign has a _ under the <
n=6 p=0.1

Use the \le construction in tex. Remove the blanks in the tags here to get it.
[ tex]p(x \le 1)[/tex ]
to get
$$p(x \le 1)$$

Thank you for your help with how to make the symbols... I also need help with the answers

nachelle said:
Thank you for your help with how to make the symbols... I also need help with the answers

$$P(x > 2) = 1 - P(x \leq 2)$$
$$P(x \leq 2) = \left( \begin{array}{c} 8 \\ 0 \end{array} \right) 0.3^0 (1-0.3)^{8-0} + \cdots$$ (sum until x = 2, including that case)

I hope you know how to carry on now.

## What is a discrete random variable?

A discrete random variable is a type of random variable that can only take on a finite or countably infinite number of values. These values are often whole numbers and are distinct from one another.

## What is a binomial random variable?

A binomial random variable is a type of discrete random variable that represents the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (usually labeled as success or failure). The probability of success remains constant throughout the trials.

## What are the characteristics of a binomial random variable?

A binomial random variable has the following characteristics:

• There is a fixed number of trials (n).
• Each trial has only two possible outcomes (success or failure).
• The probability of success (p) remains constant throughout the trials.
• The trials are independent of each other.

## What is the formula for calculating the probability of a specific outcome for a binomial random variable?

The probability of getting exactly k successes in n trials for a binomial random variable is calculated using the following formula:

P(X = k) = (nCk) * p^k * (1-p)^(n-k)

Where nCk (read as "n choose k") is the binomial coefficient, p is the probability of success, and (1-p) is the probability of failure.

## What is the expected value and variance of a binomial random variable?

The expected value (mean) of a binomial random variable is calculated by multiplying the number of trials (n) by the probability of success (p).

The variance of a binomial random variable is calculated by multiplying the number of trials (n) by the probability of success (p) and the probability of failure (1-p).

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