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...

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...

which is more likely: 9 heads in 10 tosses of a fair coin or 18 heads in 20 tosses

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...

Four red cards and four green cards are well shuffled. Cards are drawn, without replacement, until the color of a card drawn matches the color of the first card drawn. Find the average number of cards...

Suppose that Z is a standard normal random variable. Compute Pr(Z<−1.54). (If needed, round answers to 3 decimal places)

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...

a) P[Z< .62] b) P[Z < -.62] C) P[Z> 1.59] D) P[-1.3< Z< 2.61] E) P[|Z| < 1.65]

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...

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