Notes On Mean of a Random Variable - CBSE Class 12 Maths
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

#### Summary

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

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