Random Variable Resources

Suppose that the number of cars X that pass through a car wash between 4:00 P.M and 5:00 P.M on any sunny Friday has the following probability distribution(table down below):     ...

numeric: A numeric value is expected and not an expression vd=

You want to invent a gambling game in which a person rolls two (unbiased) dice and is paid some money if the sum is 7, but otherwise he loses his money. How much should you pay him for winning...

A building has two elevators, an express elevator and a standard elevator. Let X be the number of passengers using the express elevator every hour, and let Y be the number of passengers using the...

The standard error of the sample mean is calculated to \$1,475.73. The president wants to be able to estimate mean cost to within \$1,500 of the true population mean with a probability of 80%. How many...

Suppose that (Ω, F, P) is Lebesgue measure on the interval [0, 1] Define random variables X(ω)=ω, Y(ω)=2ω+3 and Z(ω)=4ω+1 Compute P(X < b ∩ Y < c) and P(Z > a) as...

With the Sample space being [0,1], suppose we are looking at a sequence of random variables Xn defined by Xωn = ωn . How can we prove that Xn converges to 0 in probability? And also what is its...

1) CBS and the NYT conducted a national poll of 1048 randomly selected 13 to 17-year olds and counted how many owned smart phones. The reporters were trying to decide whether more than half of teenagers...

I have an employee who has missed work twice in eleven years. I'm wondering if there is a way to show the probability of a random error like this occuring. Im not sure what information I may still...

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