Question

In: Statistics and Probability

You will roll two standard dice together 5 times. You are interested in the outcome where...

You will roll two standard dice together 5 times. You are interested in the outcome where both dice are six. Let X be the number of times you observe

this outcome. Answer the following questions.

1. What are the possible values for X? (values the random variable X can

take)

2. Is X binomial random variable? If so, state its parameter n and p. If

not, explain why.

3. Find the probability that you will see both dice being six at least once.

Round your answer to the three decimal places.

4. Find the mean and variance of X.

Expert Solution

1. X denotes the number of times two sixes occur .

Since total 5 rolls are performed , so the possible values for X are : 0,1,2,3,4,5

2. Yes, X is a binomial randm variable.

For X following Bnomial ( n,p ) n = 5 here.

Also, the number of all possible outcomes :

the number of ways two six can occur :

So,

3. The probability that we will see both dice being six at least once:

[Using pmf of binomial distribution]

4. The mean for a binomial (n,p) distribution is :- E[X] = n*p

Here, n = 5 ;

So,

The variance for a binomial (n,p) distribution is :- Var[X] = n*p*(1-p)

So,

.

orchestra answered 2 years ago

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