Find a formula for p(x) = P(X=x)

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In summary, the purpose of finding a formula for p(x) is to determine the probability of a random variable X taking on a specific value x. This can be useful in various fields such as statistics, economics, and science. p(x) represents the probability density function for a continuous random variable X, while P(X=x) represents the probability for a discrete random variable X. p(x) can be calculated by taking the integral of the probability density function over a specific interval of values for x. It cannot be greater than 1, as it represents the probability of an event occurring. The relationship between p(x) and the cumulative distribution function, F(x), is that p(x) is the derivative of F(x).
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Find a formula for p(x) = P(X=x) ...

So I have a test tomorrow and this question is in a list of review questions and I'm having trouble remembering where the mu fits into the formula. Any help would be greatly appreciated :)

Question: Suppose that X is a random variable with just two possible values a and b. For x = a and b find a formula for p(x) = P(X = x) in terms of a, b and mu = E(X).
 
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If P(X=a)=p and P(X=b)=1-p, what can you say about E(X)?
 

What is the purpose of finding a formula for p(x)?

The purpose of finding a formula for p(x) is to determine the probability of a random variable X taking on a specific value x. This can help in making predictions and decisions in fields such as statistics, economics, and science.

What is the difference between p(x) and P(X=x)?

p(x) represents the probability density function, which gives the probability of a continuous random variable X taking on a specific value x. P(X=x) represents the probability of a discrete random variable X taking on a specific value x.

How do you calculate p(x) for a continuous random variable?

p(x) is calculated by taking the integral of the probability density function over a specific interval of values for x. This integral represents the area under the curve of the probability density function for that interval.

Can p(x) be greater than 1?

No, p(x) cannot be greater than 1 as it represents the probability of an event occurring, which cannot exceed 100%.

What is the relationship between p(x) and the cumulative distribution function?

The cumulative distribution function, denoted as F(x), is the probability that a random variable X takes on a value less than or equal to x. The relationship between p(x) and F(x) is that p(x) is the derivative of F(x). This means that p(x) can be calculated by taking the derivative of F(x) with respect to x.

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