# statistics

posted by .

two dices are tossed once. let the random variable be t he sum of the up faces on the dice. A). find and graph the probability distribution of the random variable. and b) calculate the mean (or expectation) of this distribution

• statistics -

X=2=1+1 (1st face + 2nd face)P=1/36
X=3=1+2=2+1 P=2/36
X=4=1+3=3+1=2+2 P=3/36
X=5=1+4=4+1=2+3=3+2 P=4/36
X=6=1+5=5+1=2+4=4+2=3+3 P=5/36
X=7=1+6=6+1=2+5=5+2=3+4=4+3 P=6/36
X=8=2+6=6+2=3+5=5+3=4+4 P=5/36
X=9=3+6=6+3=4+5=5+4 P=4/36
X=10=4+6=6+4=5+5 P=3/36
X=11=5+6=6+5 P=2/36
X=12=6+6 P=1/36

Note 1/36=(1/6)*(1/6),
1/36+2/36+3/36+4/36+5/36+6/36+
5/36+4/36+3/36+2/36+1/36=36/36=1

B) m(X)=2*(1/36)+3*(2/36)+4*(3/36)+
5*(4/36)+6*(5/36)+7*(6/36)+8*(5/36)+
9*(4/36)+10*(3/36)+11*(2/36)+12*(1/36)=
(2+6+12+20+30+42+40+36+30+22+12)/36=
252/36=7

We can also use the independence of numbers on two dice. The mean of the sum
= the sum of two means: if X=X1+X2 and X1, X2 are independent then m(X1+X2)=m(X1)+m(X2)
7=3.5+3.5

## Similar Questions

1. ### Statistics

Suppose that the probability distribution of a random variable x can be described by the formula P(x) = x/15 For each of the values x = 1, 2, 3, 4, and 5. For examples, then, p(x=2) = p(2) = 2/15 a Write out the probability distribution …
2. ### Statistics

Suppose that the probability distribution of a random variable x can be described by the formula P(x) = x/15 For each of the values x = 1, 2, 3, 4, and 5. For examples, then, p(x=2) = p(2) = 2/15 a Write out the probability distribution …
3. ### STATISTICS

Consider a binomial random variable where the number of trials is 12 and the probability of success on each trial is 0.25. Find the mean and standard deviation of this random variable. I have a mean of 4 and a standard deviation of …
4. ### Statistics and Probability

A computer supply house receives a large shipment of blank CDs each week. Past experience has shown that the number of flaws per CD can be described by the following probability distribution, where the random variable X represents …
5. ### probability

A random experiment of tossing a die twice is performed. Random variable X on this sample space is defined to be the sum of two numbers turning up on the toss. Find the discrete probability distribution for the random variable X and …
6. ### Elementary statistics

Nine apples, four of which are rotten, are in a refrigerator. Three apples are randomly selected without replacement. Let the random variable x represent the number chosen that are rotten. Construct a table describing the probability …
7. ### statistics

A die has 2 red faces, 2 blue faces, and 2 green faces. It is rolled 240 times. Let R be the number of times red faces appear, and B the number of times blue faces appear. The random variable R is the sum of 240 draws at random with …
8. ### Math

Suppose a baseball player had 211 hits in a season. In the given probability distribution, the random variable X represents the number of hits the player obtained in the game. x P(x) 0 0.1879 1 0.4106 2 0.2157 3 0.1174 4 0.0624 5 0.0060 …
9. ### probability

A fair coin is flipped independently until the first Heads is observed. Let K be the number of Tails observed before the first Heads (note that K is a random variable). For k=0,1,2,…,K, let Xk be a continuous random variable that …
10. ### Statistics/probability

The random variable X has a binomial distribution with the probability of a success being 0.2 and the number of independent trials is 15. The random variable xbar is the mean of a random sample of 100 values of X. Find P(xbar<3.15).

More Similar Questions