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The expected value of the game in which 5 dice (6-sided) are rolled simultaneously is -0.2094.
<h3>How to find the mean (expectation) and variance of a random variable?</h3>Supposing that the considered random variable is discrete, we get:
Mean =
Here, n is its n data values and
is the probability of
Suppose you play a game in which 5 dice (6-sided) are rolled simultaneously.
- If a "4" is rolled, then you win $2 for each "4" showing.
- If all the dice are showing "4", you win $1000.
- If none of the dice are showing "4", then you lose $5.
Let Y is the amount of money player won. The value of X can be,
Binomial distributions consists of n independent Bernoulli trials. Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as
The probability that out of n trials, there'd be x successes is given by
The expected value and variance of X are:
Put the values as 5 trials for each time 4 appears.
The probability of loosing $5 equal probability of 0 success.
Similarly, for probability of getting profit are,
Expected value of game,
Thus, the expected value of the game in which 5 dice (6-sided) are rolled simultaneously is -0.2094.
Learn more about expectation of a random variable here:
Learn more about binomial distribution here:
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