probability distribution
Two tetrahedral dice, each with faces labelled 1, 2, 3 and 4, are thrown and the random variable X represents the sum of the numbers shown on the dice.
(i) Illustrate the distribution and describe the shape of the distribution.
It is a symetrical distribution
State the formula for expectation
E(X) = Σxp
State the formula for variance.
Var(X) = Σx2p - [E(X)]2
What is the formula of binomial distribution?
P(X) = (nCx)(px)(qn-x)
Two tetrahedral dice, each with faces labelled 1, 2, 3 and 4, are thrown and the random variable X represents the sum of the numbers shown on the dice.
(i) Find the probability distribution of X.
Two tetrahedral dice, each with faces labelled 1, 2, 3 and 4, are thrown and the random variable X represents the sum of the numbers shown on the dice.
(i) Find the probability distribution of X.
No. of people Probability
1 0.35
2 0.375
3 0.205
4 0.065
5 0.005
>5 0
Find the expected value
E(X) = 2
No. of people Probability
1 0.35
2 0.375
3 0.205
4 0.065
5 0.005
>5 0
Find the variance value
How to know if a distribution is binomial
A binomial distribution counts the number of successes in a fixed number of trials
The random variable X is given by the sum of the scores when two ordinary dice are thrown.
(i) Find the probability distribution of 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
r Pr
0 0.2
1 0.3
2 0.4
3 0.1
(i) Find the E(X2)
E(X2) = 2.8
r Pr
0 0.2
1 0.3
2 0.4
3 0.1
(i) Find the Var(X)
Var(X) = 0.84
Extensive research has shown that 1 person out of every 4 is allergic to a particular grass seed. A group of 20 university students volunteer to try out a new treatment.
(ii) What is the probability that exactly 2 people are allergic
P(X=2) = 0.067
The random variable X is given by the sum of the scores when two ordinary dice are thrown.
(i) Find P(X>8).
(ii) Find P(X=even)
(i) 5/18
(ii) 1/2
x P(X=x)
-3 0.15
-1 0.3
0 0.15
4 0.4
find the expected value
E(X) = 0.85
x P(X=x)
-3 0.15
-1 0.3
0 0.15
4 0.4
find the variance value
Var(X) = 7.3275
George wants to invest some of his monthly salary. He invests a certain amount of this every month for 18 months. For each month there is a probability of 0.25 that he will buy shares in a large company, a probability of 0.15 that he will buy shares in a small company and a probability of 0.6 that he will invest in a savings account.
(ii) Find the probability that George will buy shares in a small company in at least 3 of these 18 months.
(ii) 0.520
The probability distribution of a random variable X is given by
P(X=r) = kr for r = 1,2,3,4
(i) Find the value of constant k
(i) k=0.1
x P(X=x)
-3 a
-1 b
0 0.15
4 0.4
Given that E(X) = 0.75. Find the values of a and b
a = 0.2
b = 0.25
x P(X=x)
2 5/16
3 1/16
4 3/8
5 1/8
6 1/16
7 1/16
Find the variance value
Var(X) = 2.1875
A box contains 300 discs of different colours. There are 100 pink discs, 100 blue discs and 100 orange discs. The discs of each colour are numbered from 0 to 99. Five discs are selected at random, one at a time, with replacement. Find:
(i) the probability that no orange discs are selected
(i) 0.132