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Difference between a random variable and a probability distribution is?
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.
What is meant by probability distribution?
I will give first the non-mathematical definition as given by Triola in Elementary Statistics: A random variable is a variable typicaly represented by x that has a a single numerical value, determined by chance for each outcome of a procedure. A probability distribution is a graph, table or formula that gives the probabability for each value of the random variable. A mathematical definition given by DeGroot in "Probability and Statistics" A real valued function that is defined in space S is called a random variable. For each random variable X and each set A of real numbers, we could calculate the probabilities. The collection of all of these probabilities is the distribution of X. Triola gets accross the idea of a collection as a table, graph or formula. Further to the definition is the types of distributions- discrete or continuous. Some well know distribution are the normal distribution, exponential, binomial, uniform, triangular and Poisson.
How do you give the probability of a sum?
You find the event space for the random variable that is the required sum and then calculate the probabilities of each favourable outcome. In the simplest case it is a convolution of the probability distribution functions.
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.
If an event has a 1 in 4 chance of occurring what is the probability of it happening to one individual in a sample of five?
If we assume that the probability of an event occurring is 1 in 4 and that the event occurs to each individual independently, then the probability of the event occurring to one individual is 0.3955. In order to find this probability, we can make a random variable X which follows a Binomial distribution with 5 trials and probability of success 0.25. This makes sense because each trial is independent, the probability of success stays constant for each trial, and there are only two outcomes for each trial. Now you can find the probability by plugging into the probability mass function of the binomial distribution.
