1. A mail-order computer business has six telephone lines. Let $X$ denote the number of lines...

  

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1. A mail-order computer business has six telephone lines. Let $X$ denote the number of lines in use at probability mass function (pmf) of $X$ ix given as follows: $$ \begin{array}{1} P(x=0)=0.1 \\ P(x-1)=0.15 \\ P(x-2)=0.2 \\ P(x-3)=0.25 \\ P(x-4)=0.2 \\ P(x-5)=0.06 \\ P(x=6)=0.04 \end{array} $$ a. Determine the cumulative distribution function for this pmf. b. Calculate the probability that at least 3 lines are in use. c. Calculate the probability that at least four lines are NOT in use. d. Compute the expected value and the variance of this pmf. CS.VS.1324 1. A mail-order computer business has six telephone lines. Let $X$ denote the number of lines in use at probability mass function (pmf) of $X$ ix given as follows: $$ \begin{array}{1} P(x=0)=0.1 \\ P(x-1)=0.15 \\ P(x-2)=0.2 \\ P(x-3)=0.25 \\ P(x-4)=0.2 \\ P(x-5)=0.06 \\ P(x=6)=0.04 \end{array} $$ a. Determine the cumulative distribution function for this pmf. b. Calculate the probability that at least 3 lines are in use. c. Calculate the probability that at least four lines are NOT in use. d. Compute the expected value and the variance of this pmf. CS.VS.1324