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x 1 1.5 2.0 3.0 3.0 f(x) 0.05M 0.25M 0.15M 0.1M 0.25M Where M is a...

x 1 1.5 2.0 3.0 3.0

f(x) 0.05M 0.25M 0.15M 0.1M 0.25M

Where M is a constant. (a) Determine M so that f(x) can be a probability mass function. Using the value of M found in (a), (b) Determine and sketch F(x) (c ) Find the following probabilities: (c.1) P(X ≥ 2.0), (c.2) P(X < 1.65), (c.3) P(X = 1.5), (c.4) P(X < 1.3 or X > 2.1) (d) Find the mean and the variance of X.

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