how do I calculate the probability X1 > X2 where X1 and X2 are independent, normally distributed random variables?
how do I calculate the probability X1 > X2 where X1 and X2 are independent, normally distributed random variables?
Draw 5 cards at random from the deck. For sums < 8 you win double that sum in dollars. For 8 ≤ sum ≤ 20 you lose half your sum in dollars. If sum > 20, you lose total sum in dollars. Find the...
Draw 5 cards at random from the deck. For sums < 8 you win double that sum in dollars. For 8 ≤ sum ≤ 20 you lose half your sum in dollars. If sum > 20, you lose total sum in dollars. Find the...
Draw 5 cards at random from the deck. For sums < 8 you win double that sum in dollars. For 8 ≤ sum ≤ 20 you lose half your sum in dollars. If sum > 20, you lose total sum in dollars. Find the...
two marbles are drawn from a bag in which there are 4 red marbles and 2 blue marbles; the number of blue marbles is counted.
Introduction to Probability Distributions - Random Variables A random variable is defined as a function that associates a real number (the probability value) to an outcome of an experiment. In other words, a random variable is a generalization of the outcomes or events in a given sample space. This is possible since the random variable by definition can change so we can use the same... read more
Variance and Standard Deviation of a Random Variable We have already looked at Variance and Standard deviation as measures of dispersion under the section on Averages. We can also measure the dispersion of Random variables across a given distribution using Variance and Standard deviation. This allows us to better understand whatever the distribution represents. The Variance... read more
Expected Values of Random Variables We already looked at finding the mean in the section on averages. Random variables also have means but their means are not calculated by simply adding up the different variables. The mean of a random variable is more commonly referred to as its Expected Value, i.e. the value you expect to obtain should you carry out some experiment whose outcomes... read more
mean and variance definition in random variable in probability