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What does it mean if two variables have the same distribution?
We say that two random variables, X and Y , have the same distribution (or are equal in distribution) if they have the same p.m.f. We say that two random variables are equal, and write X = Y , if for all s in S, X(s) = Y (s). Example.
What is the distribution of X probability?
Any value x not explicitly assigned a positive probability is understood to be such that P(X=x) = 0. The function pX(x)= P(X=x) for each x within the range of X is called the probability distribution of X. It is often called the probability mass function for the discrete random variable X.
Which is the distribution of X and Y?
The functions F X ( t) = P ( X ≤ t) and F Y ( t) = P ( Y ≤ t) are termed the distribution functions of the variables X and Y, respectively. See Thanks for contributing an answer to Cross Validated!
Which is the binomial distribution for a random variable x?
The binomial distribution for a random variable X with parameters n and p represents the sum of n independent variables Z which may assume the values 0 or 1. If the probability that each Z variable assumes the value 1 is equal to p , then the mean of each variable is equal to 1*p + 0*(1-p) = p , and the variance is equal to p(1-p).
What does the mean of the same distribution mean?
It means that F X ( t) = P ( X ≤ t) = P ( Y ≤ t) = F Y ( t), for all t. Then, in particular, if the mean and variance exist, then their values coincide for these variables. The functions F X ( t) = P ( X ≤ t) and F Y ( t) = P ( Y ≤ t) are termed the distribution functions of the variables X and Y, respectively. See
Which is an example of a cumulative probability distribution?
P (X < 1) = P (X = 0) + P (X = 1) = 0.25 + 0.50 = 0.75 Like a probability distribution, a cumulative probability distribution can be represented by a table or an equation. In the table below, the cumulative probability refers to the probability than the random variable X is less than or equal to x.