Mean is the middle or average value of a random variable.
The mean of a random variable is denote by μ.
μ = ∑i=1n xipi
X or Xi |
x1 |
x2 |
x3 |
... |
xn |
P(X) or pi |
p1 |
p2 |
p3 |
... |
pn |
The mean of random variable X is also called the expectation of X, and is denoted by E(X).
E(X) = μ = ∑i=1n xipi = x1p1 + x2p2 + x3p3 + .... + xnpn
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 xi |
0 |
1 |
2 |
3 |
P(X) or pi |
1/8 |
3/8 |
3/8 |
1/8 |
μ = ∑i=14 xipi = x1p1 + x2p2 + x3p3 + x4p4
= (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 (μ) = 1.5
Mean is the middle or average value of a random variable.
The mean of a random variable is denote by μ.
μ = ∑i=1n xipi
X or Xi |
x1 |
x2 |
x3 |
... |
xn |
P(X) or pi |
p1 |
p2 |
p3 |
... |
pn |
The mean of random variable X is also called the expectation of X, and is denoted by E(X).
E(X) = μ = ∑i=1n xipi = x1p1 + x2p2 + x3p3 + .... + xnpn
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 xi |
0 |
1 |
2 |
3 |
P(X) or pi |
1/8 |
3/8 |
3/8 |
1/8 |
μ = ∑i=14 xipi = x1p1 + x2p2 + x3p3 + x4p4
= (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 (μ) = 1.5