3 A random variable has the following probability distributi

3. A random variable has the following probability distribution:

X        P(X)

0          0.05

1          0.16

2          0.16

3          0.23

4          0.40

A) Compute the expected value, variance and standard deviation of X. Show the computations for the expected value.

Solution

E(X) = (0*0.05) + (1*0.16)+(2*0.16)+(3*0.23)+(4*0.4) = 0 + 0.16 + 0.32 + 0.69 +1.6 = 2.77

E(X²) = (0²*0.05) + (1²*0.16)+(2²*0.16)+(3²*0.23)+(4²*0.4) = 0+0.16 + 0.64 + 2.07 + 6.4 = 9.27

V(X) = E(X²) - (E(X))² = 9.27 - 2.77² = 1.5971

Standard Deviation = 1.2637