Question

A 6-sides die is rolled three times. Part a: Construct the probability distribution table for the number of times the die will land on 6. Part b: Determine the expected number of times the die should land on 6

Answer 1

When we roll a die possible outcomes are 1, 2, 3, 4, 5, and 6. That is probability of getting a 6 is

p = 1/6

(a)

Let X is a random variable shows the number of times die land on 6. Here X has binomial distribution with parameter as follows:

n=3 and p=1/6

The pdf of X is

Following table shows the probability distribution:

X	P(X=x)
0	0.578704
1	0.347222
2	0.069444
3	0.00463

(b)

The  expected number of times the die should land on 6 is