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A random variable is a variable that can take different values according to a process, at least part of which is random.
For a discrete random variable (RV), a probability distribution is a function that assigns, to each value of the RV, the probability that the RV takes that value.
The probability of a continuous RV taking any specificvalue is always 0 and the distribution is a density function such that the probability of the RV taking a value between x and y is the area under the distribution function between x and y.
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What is a uniform probability distribution?
It is a probability distribution where when all of the values of a random variable occur with equal probability. Say X is the random variable, such as what number shows up when we roll a die. There are 6 possible outcomes, each with a 1/6 probability of showing up. If we create a probability distribution where X= 1,2,3,4,5, or 6, we note P(X=k)=1/k where k is any number between 1 and 6 in this case. The graph will be a rectangle.
True or False the probability that a standard normal random variable Z is between 1.50 and 2.10 is the same as the probability Z is between -2.10 and -1.50.?
It is true because the distribution is symmetrical about Z=0.
What is the difference between random variable and random variate?
Random variables is a function that can produce outcomes with different probability and random variates is the particular outcome of a random variable.
What does the normal probability density function describe?
A probability density function (pdf) for a continuous random variable (RV), is a function that describes the probability that the RV random variable will fall within a range of values. The probability of the RV falling between two values is the integral of the relevant PDF. The normal or Gaussian distribution is one of the most common distributions in probability theory. Whatever the underlying distribution of a RV, the average of a set of independent observations for that RV will by approximately Gaussian.
How does a discrete probability distribution differ from a continuous probability distribution?
A discrete probability distribution is defined over a set value (such as a value of 1 or 2 or 3, etc). A continuous probability distribution is defined over an infinite number of points (such as all values between 1 and 3, inclusive).
