Mean is the middle or average value of a random variable.
The mean of a random variable is denote by Î¼.
Î¼ = âˆ‘_{i=1}^{n} x_{i}p_{i}
X or X_{i} |
x_{1} |
x_{2} |
x_{3} |
... |
x_{n} |
P(X) or p_{i} |
p_{1} |
p_{2} |
p_{3} |
... |
p_{n} |
The mean of random variable X is also called the expectation of X, and is denoted by E(X).
E(X) = Î¼ = âˆ‘_{i=1}^{n} x_{i}p_{i} = x_{1}p_{1} + x_{2}p_{2} + x_{3}p_{3} + .... + x_{n}p_{n}
Ex:
Consider an experiment of tossing three coins simultaneously.
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
X denotes the number of heads in each outcome.
The possible values of X are 0, 1, 2 and 3.
Probability distribution of X:
X or x_{i} |
0 |
1 |
2 |
3 |
P(X) or p_{i} |
1/8 |
3/8 |
3/8 |
1/8 |
Î¼ = âˆ‘_{i=1}^{4} x_{i}p_{i} = x_{1}p_{1} + x_{2}p_{2} + x_{3}p_{3} + x_{4}p_{4}
= (0 x 1/8) + (1 x 3/8) + (2 x 3/8) + (3 x 1/8)
= 0 + 3/8+ 6/8+ 3/8
= 12/8 = 1.5
Hence, mean of random variable X (Î¼) = 1.5
Mean is the middle or average value of a random variable.
The mean of a random variable is denote by Î¼.
Î¼ = âˆ‘_{i=1}^{n} x_{i}p_{i}
X or X_{i} |
x_{1} |
x_{2} |
x_{3} |
... |
x_{n} |
P(X) or p_{i} |
p_{1} |
p_{2} |
p_{3} |
... |
p_{n} |
The mean of random variable X is also called the expectation of X, and is denoted by E(X).
E(X) = Î¼ = âˆ‘_{i=1}^{n} x_{i}p_{i} = x_{1}p_{1} + x_{2}p_{2} + x_{3}p_{3} + .... + x_{n}p_{n}
Ex:
Consider an experiment of tossing three coins simultaneously.
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
X denotes the number of heads in each outcome.
The possible values of X are 0, 1, 2 and 3.
Probability distribution of X:
X or x_{i} |
0 |
1 |
2 |
3 |
P(X) or p_{i} |
1/8 |
3/8 |
3/8 |
1/8 |
Î¼ = âˆ‘_{i=1}^{4} x_{i}p_{i} = x_{1}p_{1} + x_{2}p_{2} + x_{3}p_{3} + x_{4}p_{4}
= (0 x 1/8) + (1 x 3/8) + (2 x 3/8) + (3 x 1/8)
= 0 + 3/8+ 6/8+ 3/8
= 12/8 = 1.5
Hence, mean of random variable X (Î¼) = 1.5