Consider a random variable X with the following probability mass function (PMF) 0.10 if z 0,1, 0.30 ifz 2, 0.50 if r 3, P(z)= otherwise. (a) Verify the above is a valid PMF for the variable X. (b) By directly using the PMF above, find the mean of X. (c) By directly using the PMF above, and your result in (a), find the variance of X. (d) Using the complement rule find P(X 2).

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