Consider the discrete random variable X\displaystyle {X} given in the table below. Calculate the mean, variance, and standard deviation of X\displaystyle {X}.


X\displaystyle {X}567101118
P(X\displaystyle {X})0.070.130.140.060.490.11


μ\displaystyle \mu =
σ2\displaystyle \sigma^{{2}} =
σ\displaystyle \sigma =


Let Y\displaystyle {Y} = X+X\displaystyle {X}+{X}. Find the mean, variance, and standard deviation of Y\displaystyle {Y}.
μ\displaystyle \mu =
σ2\displaystyle \sigma^{{2}} =
σ\displaystyle \sigma =


Let Z\displaystyle {Z} = XX\displaystyle {X}-{X}. Find the mean, variance, and standard deviation of Z\displaystyle {Z}.
μ\displaystyle \mu =
σ2\displaystyle \sigma^{{2}} =
σ\displaystyle \sigma =