Using the below graph of a probability density function of random variable X, find the probability that the value of X is between 4 and 7. f(X) 10 0.2 O0.3 O04 0.5

1 Given the probability density function f(x) = over the interval [3,6], find the expected value, the mean, 3 the variance and the standard deviation. Expected value: Mean: Variance: Standard Deviation: > Next Question

Definition. When the sample space of an experiment is finite, a probability density function for a random variable is a table of all possible values of X and their corresponding probabilities. 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 event consisting of all outcomes to which the random variable eX assigns 2. 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.