(a) What are all possible values of X? b) Make a table of each of these values and the probabilities associated with them. Again, this table is called the probability density function of X.( c) Suppose that the random variable Y is 2 times the number of the head plus the number of tails flipped, find the probability density function of Yf or this experiment.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Definition. When the sample space of an experiment is finite, a
Remember that random variables assign numbers to each outcome. Each outcome has some probability of occurring. IfXis a random variable, when we write Pr[X= 2], we mean Pr[E], where E is the
To further explain this complete the following example. Suppose a fair coin is flipped 3 times. A random variable X assigns the number of heads to each outcome.
(a) What are all possible values of X?
b) Make a table of each of these values and the probabilities associated with them. Again, this table is called the probability density function of X.(
c) Suppose that the random variable Y is 2 times the number of the head plus the number of tails flipped, find the probability density function of Yf or this experiment.
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