What is the variance of a six sided die?

What is the variance of a six sided die?

When you roll a single six-sided die, the outcomes have mean 3.5 and variance 35/12, and so the corresponding mean and variance for rolling 5 dice is 5 times greater.

What is the expected value of rolling a die that has 6 sides?

A quantity equal to the average result of an experiment after a large number of trials. For example, if a fair 6-sided die is rolled, the expected value of the number rolled is 3.5. This is a correct interpretation even though it is impossible to roll a 3.5 on a 6-sided die.

What is the variance of the sum of the two dice?

How then, does this happen: Rolling one dice, results in a variance of 3512. Rolling two dice, should give a variance of 22Var(one die)=4×3512≈11.67.

What is the average number of rolls of a die to get a 6?

You need to roll the die, on the average, just four times before you see a 6. You need to roll the die, on the average, just four times before you see a 6.

How many sides are on a fair die?

six
A standard six-sided die, for example, can be considered “fair” if each of the faces has a probability of 1/6.

What does variance and deviation mean with series of die rolls?

I’m having trouble imagining what variance and deviation mean with a series of die rolls. That is, a fair die will fall with a flat distribution on all its values 1-6. Does the concept of variance really make sense on a uniform distribution? [Edit: Is it like asking “What is the variance of white noise?\\

Why does a loaded die have a smaller standard deviation?

Since the loaded die roll has a smaller standard deviation, this means that the roll of the loaded die tends to be closer to the mean (3.5) than for the fair die. When we roll the loaded die many times, we will notice a smaller spread or variation in the rolls than when we roll the fair die many times.

How to calculate the standard deviation of a random variable?

If we call the value of a die roll x, then the random variable x will have a discrete uniform distribution. That is, if we denote the probability mass function (PMF) of x by p[k] ≡ Pr [x = k], then we have p[k] = 1 K, where K is the number of distinct values k can take (i.e. here K = 6 ).

What are the variance and standard deviation for a flat distribution?

It seems the variance and standard deviation tacitly ASSUME an a priori normal distribution around an unspecified or unknown order — but a perfectly flat distribution (as n-> infinity) with no other hidden variables has no variance (or shouldn’t have any).